C4^2.9C2^3 - GroupNames

G = C₄².₉C₂³ order 128 = 2⁷

9^th non-split extension by C₄² of C₂³ acting faithfully

p-group, metabelian, nilpotent (class 3), monomial

Aliases: C₄².₉C₂³, C₈⋊Q₈.₁C₂, C₄⋊C₄.₄₄D₄, C₄⋊Q₈.₃₉C₂², C₈⋊C₄.₂C₂², C₄².₂C₂².C₂, C₂.₂₄(D₄.₈D₄), C₂².₁₉₀C₂²≀C₂, C₄².C₂.₇C₂², C₂².₅₈C₂⁴.C₂, C₂.₂₂(D₄.₁₀D₄), C₄².₃₀C₂².₄C₂, (C₂×C₄).₂₂₂(C₂×D₄), SmallGroup(128,395)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Derived series

C₁ — C₄² — C₄².₉C₂³

Chief series

C₁ — C₂ — C₂² — C₂×C₄ — C₄² — C₄².C₂ — C₂².₅₈C₂⁴ — C₄².₉C₂³

Lower central

C₁ — C₂² — C₄² — C₄².₉C₂³

Upper central

C₁ — C₂² — C₄² — C₄².₉C₂³

Jennings

C₁ — C₂² — C₂² — C₄² — C₄².₉C₂³

Generators and relations for C₄².₉C₂³
G = < a,b,c,d,e | a⁴=b⁴=1, c²=e²=a², d²=a²b², ab=ba, cac^-1=dad^-1=a^-1, eae^-1=a^-1b², cbc^-1=ebe^-1=b^-1, dbd^-1=a²b^-1, dcd^-1=ac, ece^-1=bc, de=ed >

Subgroups: 168 in 86 conjugacy classes, 30 normal (12 characteristic)
C₁, C₂, C₂, C₄, C₂², C₈, C₂×C₄, C₂×C₄, C₂×C₄, Q₈, C₄², C₄², C₄⋊C₄, C₄⋊C₄, C₂×C₈, C₂×Q₈, C₈⋊C₄, C₈⋊C₄, Q₈⋊C₄, C₄.Q₈, C₂.D₈, C₄².C₂, C₄².C₂, C₄².C₂, C₄⋊Q₈, C₄².₂C₂², C₄².₂C₂², C₄².₃₀C₂², C₈⋊Q₈, C₂².₅₈C₂⁴, C₄².₉C₂³
Quotients: C₁, C₂, C₂², D₄, C₂³, C₂×D₄, C₂²≀C₂, D₄.₈D₄, D₄.₁₀D₄, C₄².₉C₂³

Character table of C₄².₉C₂³

class	1	2A	2B	2C	4A	4B	4C	4D	4E	4F	4G	4H	4I	4J	8A	8B	8C	8D	8E	8F
size	1	1	1	1	4	4	4	8	8	8	8	8	8	16	8	8	8	8	8	8
ρ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	trivial
ρ₂	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	1	1	-1	-1	-1	-1	1	linear of order 2
ρ₃	1	1	1	1	1	1	1	1	-1	-1	1	-1	-1	-1	-1	1	1	1	1	-1	linear of order 2
ρ₄	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	linear of order 2
ρ₅	1	1	1	1	1	1	1	-1	1	-1	-1	1	-1	-1	1	-1	1	-1	1	1	linear of order 2
ρ₆	1	1	1	1	1	1	1	-1	-1	1	-1	-1	1	-1	1	1	-1	1	-1	1	linear of order 2
ρ₇	1	1	1	1	1	1	1	-1	-1	1	-1	-1	1	1	-1	-1	1	-1	1	-1	linear of order 2
ρ₈	1	1	1	1	1	1	1	-1	1	-1	-1	1	-1	1	-1	1	-1	1	-1	-1	linear of order 2
ρ₉	2	2	2	2	-2	-2	2	0	0	2	0	0	-2	0	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₀	2	2	2	2	2	-2	-2	-2	0	0	2	0	0	0	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₁	2	2	2	2	2	-2	-2	2	0	0	-2	0	0	0	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₂	2	2	2	2	-2	-2	2	0	0	-2	0	0	2	0	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₃	2	2	2	2	-2	2	-2	0	-2	0	0	2	0	0	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₄	2	2	2	2	-2	2	-2	0	2	0	0	-2	0	0	0	0	0	0	0	0	orthogonal lifted from D₄
ρ₁₅	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	-2	symplectic lifted from D₄.₁₀D₄, Schur index 2
ρ₁₆	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	-2	0	0	0	0	2	symplectic lifted from D₄.₁₀D₄, Schur index 2
ρ₁₇	4	4	-4	-4	0	0	0	0	0	0	0	0	0	0	0	2	0	-2	0	0	symplectic lifted from D₄.₁₀D₄, Schur index 2
ρ₁₈	4	4	-4	-4	0	0	0	0	0	0	0	0	0	0	0	-2	0	2	0	0	symplectic lifted from D₄.₁₀D₄, Schur index 2
ρ₁₉	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	2i	0	-2i	0	complex lifted from D₄.₈D₄
ρ₂₀	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	-2i	0	2i	0	complex lifted from D₄.₈D₄

Smallest permutation representation of C₄².₉C₂³
►Regular action on 128 points

Generators in S₁₂₈

(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)(25 26 27 28)(29 30 31 32)(33 34 35 36)(37 38 39 40)(41 42 43 44)(45 46 47 48)(49 50 51 52)(53 54 55 56)(57 58 59 60)(61 62 63 64)(65 66 67 68)(69 70 71 72)(73 74 75 76)(77 78 79 80)(81 82 83 84)(85 86 87 88)(89 90 91 92)(93 94 95 96)(97 98 99 100)(101 102 103 104)(105 106 107 108)(109 110 111 112)(113 114 115 116)(117 118 119 120)(121 122 123 124)(125 126 127 128)

(1 20 13 5)(2 17 14 6)(3 18 15 7)(4 19 16 8)(9 121 118 128)(10 122 119 125)(11 123 120 126)(12 124 117 127)(21 29 35 26)(22 30 36 27)(23 31 33 28)(24 32 34 25)(37 42 47 50)(38 43 48 51)(39 44 45 52)(40 41 46 49)(53 58 67 63)(54 59 68 64)(55 60 65 61)(56 57 66 62)(69 76 79 84)(70 73 80 81)(71 74 77 82)(72 75 78 83)(85 92 97 93)(86 89 98 94)(87 90 99 95)(88 91 100 96)(101 116 111 106)(102 113 112 107)(103 114 109 108)(104 115 110 105)

(1 71 3 69)(2 70 4 72)(5 74 7 76)(6 73 8 75)(9 68 11 66)(10 67 12 65)(13 77 15 79)(14 80 16 78)(17 81 19 83)(18 84 20 82)(21 85 23 87)(22 88 24 86)(25 89 27 91)(26 92 28 90)(29 93 31 95)(30 96 32 94)(33 99 35 97)(34 98 36 100)(37 101 39 103)(38 104 40 102)(41 107 43 105)(42 106 44 108)(45 109 47 111)(46 112 48 110)(49 113 51 115)(50 116 52 114)(53 117 55 119)(54 120 56 118)(57 121 59 123)(58 124 60 122)(61 125 63 127)(62 128 64 126)

(1 45 15 37)(2 48 16 40)(3 47 13 39)(4 46 14 38)(5 50 18 44)(6 49 19 43)(7 52 20 42)(8 51 17 41)(9 97 120 87)(10 100 117 86)(11 99 118 85)(12 98 119 88)(21 67 33 55)(22 66 34 54)(23 65 35 53)(24 68 36 56)(25 62 30 59)(26 61 31 58)(27 64 32 57)(28 63 29 60)(69 110 77 102)(70 109 78 101)(71 112 79 104)(72 111 80 103)(73 116 83 108)(74 115 84 107)(75 114 81 106)(76 113 82 105)(89 127 96 122)(90 126 93 121)(91 125 94 124)(92 128 95 123)

(1 29 3 31)(2 25 4 27)(5 35 7 33)(6 24 8 22)(9 102 11 104)(10 111 12 109)(13 26 15 28)(14 32 16 30)(17 34 19 36)(18 23 20 21)(37 63 39 61)(38 57 40 59)(41 54 43 56)(42 67 44 65)(45 60 47 58)(46 64 48 62)(49 68 51 66)(50 53 52 55)(69 99 71 97)(70 86 72 88)(73 94 75 96)(74 92 76 90)(77 85 79 87)(78 100 80 98)(81 89 83 91)(82 93 84 95)(101 117 103 119)(105 121 107 123)(106 127 108 125)(110 118 112 120)(113 126 115 128)(114 122 116 124)

G:=sub<Sym(128)| (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84)(85,86,87,88)(89,90,91,92)(93,94,95,96)(97,98,99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)(121,122,123,124)(125,126,127,128), (1,20,13,5)(2,17,14,6)(3,18,15,7)(4,19,16,8)(9,121,118,128)(10,122,119,125)(11,123,120,126)(12,124,117,127)(21,29,35,26)(22,30,36,27)(23,31,33,28)(24,32,34,25)(37,42,47,50)(38,43,48,51)(39,44,45,52)(40,41,46,49)(53,58,67,63)(54,59,68,64)(55,60,65,61)(56,57,66,62)(69,76,79,84)(70,73,80,81)(71,74,77,82)(72,75,78,83)(85,92,97,93)(86,89,98,94)(87,90,99,95)(88,91,100,96)(101,116,111,106)(102,113,112,107)(103,114,109,108)(104,115,110,105), (1,71,3,69)(2,70,4,72)(5,74,7,76)(6,73,8,75)(9,68,11,66)(10,67,12,65)(13,77,15,79)(14,80,16,78)(17,81,19,83)(18,84,20,82)(21,85,23,87)(22,88,24,86)(25,89,27,91)(26,92,28,90)(29,93,31,95)(30,96,32,94)(33,99,35,97)(34,98,36,100)(37,101,39,103)(38,104,40,102)(41,107,43,105)(42,106,44,108)(45,109,47,111)(46,112,48,110)(49,113,51,115)(50,116,52,114)(53,117,55,119)(54,120,56,118)(57,121,59,123)(58,124,60,122)(61,125,63,127)(62,128,64,126), (1,45,15,37)(2,48,16,40)(3,47,13,39)(4,46,14,38)(5,50,18,44)(6,49,19,43)(7,52,20,42)(8,51,17,41)(9,97,120,87)(10,100,117,86)(11,99,118,85)(12,98,119,88)(21,67,33,55)(22,66,34,54)(23,65,35,53)(24,68,36,56)(25,62,30,59)(26,61,31,58)(27,64,32,57)(28,63,29,60)(69,110,77,102)(70,109,78,101)(71,112,79,104)(72,111,80,103)(73,116,83,108)(74,115,84,107)(75,114,81,106)(76,113,82,105)(89,127,96,122)(90,126,93,121)(91,125,94,124)(92,128,95,123), (1,29,3,31)(2,25,4,27)(5,35,7,33)(6,24,8,22)(9,102,11,104)(10,111,12,109)(13,26,15,28)(14,32,16,30)(17,34,19,36)(18,23,20,21)(37,63,39,61)(38,57,40,59)(41,54,43,56)(42,67,44,65)(45,60,47,58)(46,64,48,62)(49,68,51,66)(50,53,52,55)(69,99,71,97)(70,86,72,88)(73,94,75,96)(74,92,76,90)(77,85,79,87)(78,100,80,98)(81,89,83,91)(82,93,84,95)(101,117,103,119)(105,121,107,123)(106,127,108,125)(110,118,112,120)(113,126,115,128)(114,122,116,124)>;

G:=Group( (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84)(85,86,87,88)(89,90,91,92)(93,94,95,96)(97,98,99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)(121,122,123,124)(125,126,127,128), (1,20,13,5)(2,17,14,6)(3,18,15,7)(4,19,16,8)(9,121,118,128)(10,122,119,125)(11,123,120,126)(12,124,117,127)(21,29,35,26)(22,30,36,27)(23,31,33,28)(24,32,34,25)(37,42,47,50)(38,43,48,51)(39,44,45,52)(40,41,46,49)(53,58,67,63)(54,59,68,64)(55,60,65,61)(56,57,66,62)(69,76,79,84)(70,73,80,81)(71,74,77,82)(72,75,78,83)(85,92,97,93)(86,89,98,94)(87,90,99,95)(88,91,100,96)(101,116,111,106)(102,113,112,107)(103,114,109,108)(104,115,110,105), (1,71,3,69)(2,70,4,72)(5,74,7,76)(6,73,8,75)(9,68,11,66)(10,67,12,65)(13,77,15,79)(14,80,16,78)(17,81,19,83)(18,84,20,82)(21,85,23,87)(22,88,24,86)(25,89,27,91)(26,92,28,90)(29,93,31,95)(30,96,32,94)(33,99,35,97)(34,98,36,100)(37,101,39,103)(38,104,40,102)(41,107,43,105)(42,106,44,108)(45,109,47,111)(46,112,48,110)(49,113,51,115)(50,116,52,114)(53,117,55,119)(54,120,56,118)(57,121,59,123)(58,124,60,122)(61,125,63,127)(62,128,64,126), (1,45,15,37)(2,48,16,40)(3,47,13,39)(4,46,14,38)(5,50,18,44)(6,49,19,43)(7,52,20,42)(8,51,17,41)(9,97,120,87)(10,100,117,86)(11,99,118,85)(12,98,119,88)(21,67,33,55)(22,66,34,54)(23,65,35,53)(24,68,36,56)(25,62,30,59)(26,61,31,58)(27,64,32,57)(28,63,29,60)(69,110,77,102)(70,109,78,101)(71,112,79,104)(72,111,80,103)(73,116,83,108)(74,115,84,107)(75,114,81,106)(76,113,82,105)(89,127,96,122)(90,126,93,121)(91,125,94,124)(92,128,95,123), (1,29,3,31)(2,25,4,27)(5,35,7,33)(6,24,8,22)(9,102,11,104)(10,111,12,109)(13,26,15,28)(14,32,16,30)(17,34,19,36)(18,23,20,21)(37,63,39,61)(38,57,40,59)(41,54,43,56)(42,67,44,65)(45,60,47,58)(46,64,48,62)(49,68,51,66)(50,53,52,55)(69,99,71,97)(70,86,72,88)(73,94,75,96)(74,92,76,90)(77,85,79,87)(78,100,80,98)(81,89,83,91)(82,93,84,95)(101,117,103,119)(105,121,107,123)(106,127,108,125)(110,118,112,120)(113,126,115,128)(114,122,116,124) );

G=PermutationGroup([[(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24),(25,26,27,28),(29,30,31,32),(33,34,35,36),(37,38,39,40),(41,42,43,44),(45,46,47,48),(49,50,51,52),(53,54,55,56),(57,58,59,60),(61,62,63,64),(65,66,67,68),(69,70,71,72),(73,74,75,76),(77,78,79,80),(81,82,83,84),(85,86,87,88),(89,90,91,92),(93,94,95,96),(97,98,99,100),(101,102,103,104),(105,106,107,108),(109,110,111,112),(113,114,115,116),(117,118,119,120),(121,122,123,124),(125,126,127,128)], [(1,20,13,5),(2,17,14,6),(3,18,15,7),(4,19,16,8),(9,121,118,128),(10,122,119,125),(11,123,120,126),(12,124,117,127),(21,29,35,26),(22,30,36,27),(23,31,33,28),(24,32,34,25),(37,42,47,50),(38,43,48,51),(39,44,45,52),(40,41,46,49),(53,58,67,63),(54,59,68,64),(55,60,65,61),(56,57,66,62),(69,76,79,84),(70,73,80,81),(71,74,77,82),(72,75,78,83),(85,92,97,93),(86,89,98,94),(87,90,99,95),(88,91,100,96),(101,116,111,106),(102,113,112,107),(103,114,109,108),(104,115,110,105)], [(1,71,3,69),(2,70,4,72),(5,74,7,76),(6,73,8,75),(9,68,11,66),(10,67,12,65),(13,77,15,79),(14,80,16,78),(17,81,19,83),(18,84,20,82),(21,85,23,87),(22,88,24,86),(25,89,27,91),(26,92,28,90),(29,93,31,95),(30,96,32,94),(33,99,35,97),(34,98,36,100),(37,101,39,103),(38,104,40,102),(41,107,43,105),(42,106,44,108),(45,109,47,111),(46,112,48,110),(49,113,51,115),(50,116,52,114),(53,117,55,119),(54,120,56,118),(57,121,59,123),(58,124,60,122),(61,125,63,127),(62,128,64,126)], [(1,45,15,37),(2,48,16,40),(3,47,13,39),(4,46,14,38),(5,50,18,44),(6,49,19,43),(7,52,20,42),(8,51,17,41),(9,97,120,87),(10,100,117,86),(11,99,118,85),(12,98,119,88),(21,67,33,55),(22,66,34,54),(23,65,35,53),(24,68,36,56),(25,62,30,59),(26,61,31,58),(27,64,32,57),(28,63,29,60),(69,110,77,102),(70,109,78,101),(71,112,79,104),(72,111,80,103),(73,116,83,108),(74,115,84,107),(75,114,81,106),(76,113,82,105),(89,127,96,122),(90,126,93,121),(91,125,94,124),(92,128,95,123)], [(1,29,3,31),(2,25,4,27),(5,35,7,33),(6,24,8,22),(9,102,11,104),(10,111,12,109),(13,26,15,28),(14,32,16,30),(17,34,19,36),(18,23,20,21),(37,63,39,61),(38,57,40,59),(41,54,43,56),(42,67,44,65),(45,60,47,58),(46,64,48,62),(49,68,51,66),(50,53,52,55),(69,99,71,97),(70,86,72,88),(73,94,75,96),(74,92,76,90),(77,85,79,87),(78,100,80,98),(81,89,83,91),(82,93,84,95),(101,117,103,119),(105,121,107,123),(106,127,108,125),(110,118,112,120),(113,126,115,128),(114,122,116,124)]])

Matrix representation of C₄².₉C₂³ ►in GL₈(𝔽₁₇)

1	0	15	0	0	0	0	0
0	0	16	1	0	0	0	0
1	0	16	0	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	0	1	0
0	0	0	0	4	16	4	0
0	0	0	0	1	0	0	0
0	0	0	0	11	10	0	1

1	15	0	0	0	0	0	0
1	16	0	0	0	0	0	0
0	16	0	1	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	16	0	0	0
0	0	0	0	4	16	4	0
0	0	0	0	12	0	12	13

9	8	1	12	0	0	0	0
2	10	3	15	0	0	0	0
7	15	15	10	0	0	0	0
4	13	13	0	0	0	0	0
0	0	0	0	8	0	2	8
0	0	0	0	15	11	15	15
0	0	0	0	5	12	8	8
0	0	0	0	10	14	13	7

7	9	3	12	0	0	0	0
15	15	16	13	0	0	0	0
6	7	8	2	0	0	0	0
13	3	14	4	0	0	0	0
0	0	0	0	2	8	6	15
0	0	0	0	8	4	0	9
0	0	0	0	16	6	0	15
0	0	0	0	6	8	6	11

9	12	2	3	0	0	0	0
8	14	8	11	0	0	0	0
6	16	10	4	0	0	0	0
16	5	12	1	0	0	0	0
0	0	0	0	0	0	0	1
0	0	0	0	5	0	5	4
0	0	0	0	6	7	0	16
0	0	0	0	1	0	0	0

G:=sub<GL(8,GF(17))| [1,0,1,1,0,0,0,0,0,0,0,16,0,0,0,0,15,16,16,16,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,4,1,11,0,0,0,0,0,16,0,10,0,0,0,0,1,4,0,0,0,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,15,16,16,16,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,4,12,0,0,0,0,1,0,16,0,0,0,0,0,0,0,4,12,0,0,0,0,0,0,0,13],[9,2,7,4,0,0,0,0,8,10,15,13,0,0,0,0,1,3,15,13,0,0,0,0,12,15,10,0,0,0,0,0,0,0,0,0,8,15,5,10,0,0,0,0,0,11,12,14,0,0,0,0,2,15,8,13,0,0,0,0,8,15,8,7],[7,15,6,13,0,0,0,0,9,15,7,3,0,0,0,0,3,16,8,14,0,0,0,0,12,13,2,4,0,0,0,0,0,0,0,0,2,8,16,6,0,0,0,0,8,4,6,8,0,0,0,0,6,0,0,6,0,0,0,0,15,9,15,11],[9,8,6,16,0,0,0,0,12,14,16,5,0,0,0,0,2,8,10,12,0,0,0,0,3,11,4,1,0,0,0,0,0,0,0,0,0,5,6,1,0,0,0,0,0,0,7,0,0,0,0,0,0,5,0,0,0,0,0,0,1,4,16,0] >;

C₄².₉C₂³ in GAP, Magma, Sage, TeX

C_4^2._9C_2^3

% in TeX

G:=Group("C4^2.9C2^3");

// GroupNames label

G:=SmallGroup(128,395);

// by ID

G=gap.SmallGroup(128,395);

# by ID

G:=PCGroup([7,-2,2,2,-2,2,-2,2,224,141,456,422,184,1123,570,521,136,3924,1411,998,242]);

// Polycyclic

G:=Group<a,b,c,d,e|a^4=b^4=1,c^2=e^2=a^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,e*a*e^-1=a^-1*b^2,c*b*c^-1=e*b*e^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=a*c,e*c*e^-1=b*c,d*e=e*d>;

// generators/relations

Export

Character table of C₄².₉C₂³ in TeX

1	0	15	0	0	0	0	0
0	0	16	1	0	0	0	0
1	0	16	0	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	0	1	0
0	0	0	0	4	16	4	0
0	0	0	0	1	0	0	0
0	0	0	0	11	10	0	1

1	15	0	0	0	0	0	0
1	16	0	0	0	0	0	0
0	16	0	1	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	16	0	0	0
0	0	0	0	4	16	4	0
0	0	0	0	12	0	12	13

9	8	1	12	0	0	0	0
2	10	3	15	0	0	0	0
7	15	15	10	0	0	0	0
4	13	13	0	0	0	0	0
0	0	0	0	8	0	2	8
0	0	0	0	15	11	15	15
0	0	0	0	5	12	8	8
0	0	0	0	10	14	13	7

7	9	3	12	0	0	0	0
15	15	16	13	0	0	0	0
6	7	8	2	0	0	0	0
13	3	14	4	0	0	0	0
0	0	0	0	2	8	6	15
0	0	0	0	8	4	0	9
0	0	0	0	16	6	0	15
0	0	0	0	6	8	6	11

9	12	2	3	0	0	0	0
8	14	8	11	0	0	0	0
6	16	10	4	0	0	0	0
16	5	12	1	0	0	0	0
0	0	0	0	0	0	0	1
0	0	0	0	5	0	5	4
0	0	0	0	6	7	0	16
0	0	0	0	1	0	0	0

1	0	15	0	0	0	0	0
0	0	16	1	0	0	0	0
1	0	16	0	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	0	1	0
0	0	0	0	4	16	4	0
0	0	0	0	1	0	0	0
0	0	0	0	11	10	0	1

1	15	0	0	0	0	0	0
1	16	0	0	0	0	0	0
0	16	0	1	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	16	0	0	0
0	0	0	0	4	16	4	0
0	0	0	0	12	0	12	13

9	8	1	12	0	0	0	0
2	10	3	15	0	0	0	0
7	15	15	10	0	0	0	0
4	13	13	0	0	0	0	0
0	0	0	0	8	0	2	8
0	0	0	0	15	11	15	15
0	0	0	0	5	12	8	8
0	0	0	0	10	14	13	7

7	9	3	12	0	0	0	0
15	15	16	13	0	0	0	0
6	7	8	2	0	0	0	0
13	3	14	4	0	0	0	0
0	0	0	0	2	8	6	15
0	0	0	0	8	4	0	9
0	0	0	0	16	6	0	15
0	0	0	0	6	8	6	11

9	12	2	3	0	0	0	0
8	14	8	11	0	0	0	0
6	16	10	4	0	0	0	0
16	5	12	1	0	0	0	0
0	0	0	0	0	0	0	1
0	0	0	0	5	0	5	4
0	0	0	0	6	7	0	16
0	0	0	0	1	0	0	0

G = C42.9C23 order 128 = 27

9th non-split extension by C42 of C23 acting faithfully

G = C₄².₉C₂³ order 128 = 2⁷

9^th non-split extension by C₄² of C₂³ acting faithfully

1	0	15	0	0	0	0	0
0	0	16	1	0	0	0	0
1	0	16	0	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	0	1	0
0	0	0	0	4	16	4	0
0	0	0	0	1	0	0	0
0	0	0	0	11	10	0	1

1	15	0	0	0	0	0	0
1	16	0	0	0	0	0	0
0	16	0	1	0	0	0	0
1	16	16	0	0	0	0	0
0	0	0	0	0	1	0	0
0	0	0	0	16	0	0	0
0	0	0	0	4	16	4	0
0	0	0	0	12	0	12	13

9	8	1	12	0	0	0	0
2	10	3	15	0	0	0	0
7	15	15	10	0	0	0	0
4	13	13	0	0	0	0	0
0	0	0	0	8	0	2	8
0	0	0	0	15	11	15	15
0	0	0	0	5	12	8	8
0	0	0	0	10	14	13	7

7	9	3	12	0	0	0	0
15	15	16	13	0	0	0	0
6	7	8	2	0	0	0	0
13	3	14	4	0	0	0	0
0	0	0	0	2	8	6	15
0	0	0	0	8	4	0	9
0	0	0	0	16	6	0	15
0	0	0	0	6	8	6	11

9	12	2	3	0	0	0	0
8	14	8	11	0	0	0	0
6	16	10	4	0	0	0	0
16	5	12	1	0	0	0	0
0	0	0	0	0	0	0	1
0	0	0	0	5	0	5	4
0	0	0	0	6	7	0	16
0	0	0	0	1	0	0	0