C9:C16 - GroupNames

(1 92 136 61 114 107 77 23 48)(2 33 24 78 108 115 62 137 93)(3 94 138 63 116 109 79 25 34)(4 35 26 80 110 117 64 139 95)(5 96 140 49 118 111 65 27 36)(6 37 28 66 112 119 50 141 81)(7 82 142 51 120 97 67 29 38)(8 39 30 68 98 121 52 143 83)(9 84 144 53 122 99 69 31 40)(10 41 32 70 100 123 54 129 85)(11 86 130 55 124 101 71 17 42)(12 43 18 72 102 125 56 131 87)(13 88 132 57 126 103 73 19 44)(14 45 20 74 104 127 58 133 89)(15 90 134 59 128 105 75 21 46)(16 47 22 76 106 113 60 135 91)

(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)(129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144)

G:=sub<Sym(144)| (1,92,136,61,114,107,77,23,48)(2,33,24,78,108,115,62,137,93)(3,94,138,63,116,109,79,25,34)(4,35,26,80,110,117,64,139,95)(5,96,140,49,118,111,65,27,36)(6,37,28,66,112,119,50,141,81)(7,82,142,51,120,97,67,29,38)(8,39,30,68,98,121,52,143,83)(9,84,144,53,122,99,69,31,40)(10,41,32,70,100,123,54,129,85)(11,86,130,55,124,101,71,17,42)(12,43,18,72,102,125,56,131,87)(13,88,132,57,126,103,73,19,44)(14,45,20,74,104,127,58,133,89)(15,90,134,59,128,105,75,21,46)(16,47,22,76,106,113,60,135,91), (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)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)>;

G:=Group( (1,92,136,61,114,107,77,23,48)(2,33,24,78,108,115,62,137,93)(3,94,138,63,116,109,79,25,34)(4,35,26,80,110,117,64,139,95)(5,96,140,49,118,111,65,27,36)(6,37,28,66,112,119,50,141,81)(7,82,142,51,120,97,67,29,38)(8,39,30,68,98,121,52,143,83)(9,84,144,53,122,99,69,31,40)(10,41,32,70,100,123,54,129,85)(11,86,130,55,124,101,71,17,42)(12,43,18,72,102,125,56,131,87)(13,88,132,57,126,103,73,19,44)(14,45,20,74,104,127,58,133,89)(15,90,134,59,128,105,75,21,46)(16,47,22,76,106,113,60,135,91), (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)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144) );

G=PermutationGroup([[(1,92,136,61,114,107,77,23,48),(2,33,24,78,108,115,62,137,93),(3,94,138,63,116,109,79,25,34),(4,35,26,80,110,117,64,139,95),(5,96,140,49,118,111,65,27,36),(6,37,28,66,112,119,50,141,81),(7,82,142,51,120,97,67,29,38),(8,39,30,68,98,121,52,143,83),(9,84,144,53,122,99,69,31,40),(10,41,32,70,100,123,54,129,85),(11,86,130,55,124,101,71,17,42),(12,43,18,72,102,125,56,131,87),(13,88,132,57,126,103,73,19,44),(14,45,20,74,104,127,58,133,89),(15,90,134,59,128,105,75,21,46),(16,47,22,76,106,113,60,135,91)], [(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),(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)]])

C₉⋊C₁₆ is a maximal subgroup of
C₁₆×D₉ C₁₆⋊D₉ C₃₆.C₈ C₉⋊D₁₆ D₈.D₉ C₉⋊SD₃₂ C₉⋊Q₃₂ C₂₇⋊C₁₆ C₉⋊C₄₈ C₇₂.S₃
C₉⋊C₁₆ is a maximal quotient of
C₉⋊C₃₂ C₂₇⋊C₁₆ C₇₂.S₃

48 conjugacy classes

class	1	2	3	4A	4B	6	8A	8B	8C	8D	9A	9B	9C	12A	12B	16A	···	16H	18A	18B	18C	24A	24B	24C	24D	36A	···	36F	72A	···	72L
order	1	2	3	4	4	6	8	8	8	8	9	9	9	12	12	16	···	16	18	18	18	24	24	24	24	36	···	36	72	···	72
size	1	1	2	1	1	2	1	1	1	1	2	2	2	2	2	9	···	9	2	2	2	2	2	2	2	2	···	2	2	···	2

48 irreducible representations

dim	1	1	1	1	1	2	2	2	2	2	2	2	2
type	+	+				+	-	+		-
image	C₁	C₂	C₄	C₈	C₁₆	S₃	Dic₃	D₉	C₃⋊C₈	Dic₉	C₃⋊C₁₆	C₉⋊C₈	C₉⋊C₁₆
kernel	C₉⋊C₁₆	C₇₂	C₃₆	C₁₈	C₉	C₂₄	C₁₂	C₈	C₆	C₄	C₃	C₂	C₁
# reps	1	1	2	4	8	1	1	3	2	3	4	6	12

Matrix representation of C₉⋊C₁₆ ►in GL₂(𝔽₁₇) generated by

6	14
7	8

7	2
0	10

G:=sub<GL(2,GF(17))| [6,7,14,8],[7,0,2,10] >;

C₉⋊C₁₆ in GAP, Magma, Sage, TeX

C_9\rtimes C_{16}

% in TeX

G:=Group("C9:C16");

// GroupNames label

G:=SmallGroup(144,1);

// by ID

G=gap.SmallGroup(144,1);

# by ID

G:=PCGroup([6,-2,-2,-2,-2,-3,-3,12,31,50,2404,208,3461]);

// Polycyclic

G:=Group<a,b|a^9=b^16=1,b*a*b^-1=a^-1>;

// generators/relations

Export

Subgroup lattice of C₉⋊C₁₆ in TeX

G = C9⋊C16 order 144 = 24·32

The semidirect product of C9 and C16 acting via C16/C8=C2

G = C₉⋊C₁₆ order 144 = 2⁴·3²

The semidirect product of C₉ and C₁₆ acting via C₁₆/C₈=C₂