p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.73C23, C4.1492+ 1+4, C4⋊C4.185D4, C8⋊4Q8⋊20C2, Q8⋊3Q8⋊13C2, C4⋊2Q16⋊44C2, C4⋊Q16⋊24C2, C8.20(C4○D4), (C2×Q8).253D4, C2.72(Q8○D8), (C4×SD16).8C2, C8.2D4.3C2, Q16⋊C4⋊30C2, C4⋊C4.449C23, C4⋊C8.151C22, (C2×C4).590C24, (C4×C8).208C22, (C2×C8).222C23, D4.D4.2C2, C4⋊Q8.217C22, Q8.D4.4C2, C8⋊C4.77C22, C2.44(Q8⋊6D4), (C4×D4).223C22, (C2×D4).284C23, C4.54(C8.C22), (C2×Q16).94C22, (C2×Q8).269C23, (C4×Q8).213C22, C4.Q8.141C22, Q8⋊C4.95C22, (C2×SD16).76C22, C4.4D4.90C22, C22.850(C22×D4), D4⋊C4.177C22, C22.50C24.11C2, C4.168(C2×C4○D4), (C2×C4).654(C2×D4), C2.92(C2×C8.C22), SmallGroup(128,2130)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.73C23
G = < a,b,c,d,e | a4=b4=1, c2=b2, d2=e2=a2, ab=ba, cac-1=eae-1=a-1, dad-1=ab2, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ce=ec, de=ed >
Subgroups: 304 in 175 conjugacy classes, 88 normal (38 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C8, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, Q16, C22×C4, C2×D4, C2×Q8, C2×Q8, C4×C8, C8⋊C4, D4⋊C4, Q8⋊C4, Q8⋊C4, C4⋊C8, C4⋊C8, C4.Q8, C42⋊C2, C4×D4, C4×Q8, C4×Q8, C4×Q8, C22⋊Q8, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, C4⋊Q8, C2×SD16, C2×SD16, C2×Q16, C4×SD16, Q16⋊C4, C8⋊4Q8, D4.D4, C4⋊2Q16, C4⋊2Q16, Q8.D4, C4⋊Q16, C8.2D4, C22.50C24, Q8⋊3Q8, C42.73C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, C24, C8.C22, C22×D4, C2×C4○D4, 2+ 1+4, Q8⋊6D4, C2×C8.C22, Q8○D8, C42.73C23
Character table of C42.73C23
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 8A | 8B | 8C | 8D | 8E | 8F | |
| size | 1 | 1 | 1 | 1 | 8 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | 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 | 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 | 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 | -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 | -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 | -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 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | linear of order 2 |
| ρ9 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | linear of order 2 |
| ρ10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 2 |
| ρ11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | linear of order 2 |
| ρ12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ13 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | linear of order 2 |
| ρ14 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ15 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | linear of order 2 |
| ρ16 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 2 |
| ρ17 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | 2 | 2 | 0 | 2 | 2 | -2 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | -2 | -2 | 0 | -2 | 2 | 2 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | -2 | -2 | 0 | 2 | -2 | 2 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ20 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | 2 | 2 | 0 | -2 | -2 | -2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ21 | 2 | -2 | 2 | -2 | 0 | 2 | -2 | 0 | 0 | -2i | 0 | 0 | 0 | -2i | 0 | 0 | 2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 2 | -2 | 0 | 0 | 2i | 0 | 0 | 0 | 2i | 0 | 0 | -2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 2 | -2 | 0 | 0 | 2i | 0 | 0 | 0 | -2i | 0 | 0 | -2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 2 | -2 | 0 | 0 | -2i | 0 | 0 | 0 | 2i | 0 | 0 | 2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ25 | 4 | -4 | 4 | -4 | 0 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 2+ 1+4 |
| ρ26 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ27 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ28 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√2 | 0 | 0 | -2√2 | 0 | 0 | symplectic lifted from Q8○D8, Schur index 2 |
| ρ29 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√2 | 0 | 0 | 2√2 | 0 | 0 | symplectic lifted from Q8○D8, Schur index 2 |
►On 64 points
Generators in S64
(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)
(1 51 11 25)(2 52 12 26)(3 49 9 27)(4 50 10 28)(5 62 54 58)(6 63 55 59)(7 64 56 60)(8 61 53 57)(13 37 35 31)(14 38 36 32)(15 39 33 29)(16 40 34 30)(17 48 44 23)(18 45 41 24)(19 46 42 21)(20 47 43 22)
(1 59 11 63)(2 58 12 62)(3 57 9 61)(4 60 10 64)(5 52 54 26)(6 51 55 25)(7 50 56 28)(8 49 53 27)(13 22 35 47)(14 21 36 46)(15 24 33 45)(16 23 34 48)(17 40 44 30)(18 39 41 29)(19 38 42 32)(20 37 43 31)
(1 37 3 39)(2 32 4 30)(5 42 7 44)(6 20 8 18)(9 29 11 31)(10 40 12 38)(13 49 15 51)(14 28 16 26)(17 54 19 56)(21 60 23 58)(22 61 24 63)(25 35 27 33)(34 52 36 50)(41 55 43 53)(45 59 47 57)(46 64 48 62)
(1 39 3 37)(2 38 4 40)(5 21 7 23)(6 24 8 22)(9 31 11 29)(10 30 12 32)(13 25 15 27)(14 28 16 26)(17 62 19 64)(18 61 20 63)(33 49 35 51)(34 52 36 50)(41 57 43 59)(42 60 44 58)(45 53 47 55)(46 56 48 54)
G:=sub<Sym(64)| (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), (1,51,11,25)(2,52,12,26)(3,49,9,27)(4,50,10,28)(5,62,54,58)(6,63,55,59)(7,64,56,60)(8,61,53,57)(13,37,35,31)(14,38,36,32)(15,39,33,29)(16,40,34,30)(17,48,44,23)(18,45,41,24)(19,46,42,21)(20,47,43,22), (1,59,11,63)(2,58,12,62)(3,57,9,61)(4,60,10,64)(5,52,54,26)(6,51,55,25)(7,50,56,28)(8,49,53,27)(13,22,35,47)(14,21,36,46)(15,24,33,45)(16,23,34,48)(17,40,44,30)(18,39,41,29)(19,38,42,32)(20,37,43,31), (1,37,3,39)(2,32,4,30)(5,42,7,44)(6,20,8,18)(9,29,11,31)(10,40,12,38)(13,49,15,51)(14,28,16,26)(17,54,19,56)(21,60,23,58)(22,61,24,63)(25,35,27,33)(34,52,36,50)(41,55,43,53)(45,59,47,57)(46,64,48,62), (1,39,3,37)(2,38,4,40)(5,21,7,23)(6,24,8,22)(9,31,11,29)(10,30,12,32)(13,25,15,27)(14,28,16,26)(17,62,19,64)(18,61,20,63)(33,49,35,51)(34,52,36,50)(41,57,43,59)(42,60,44,58)(45,53,47,55)(46,56,48,54)>;
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), (1,51,11,25)(2,52,12,26)(3,49,9,27)(4,50,10,28)(5,62,54,58)(6,63,55,59)(7,64,56,60)(8,61,53,57)(13,37,35,31)(14,38,36,32)(15,39,33,29)(16,40,34,30)(17,48,44,23)(18,45,41,24)(19,46,42,21)(20,47,43,22), (1,59,11,63)(2,58,12,62)(3,57,9,61)(4,60,10,64)(5,52,54,26)(6,51,55,25)(7,50,56,28)(8,49,53,27)(13,22,35,47)(14,21,36,46)(15,24,33,45)(16,23,34,48)(17,40,44,30)(18,39,41,29)(19,38,42,32)(20,37,43,31), (1,37,3,39)(2,32,4,30)(5,42,7,44)(6,20,8,18)(9,29,11,31)(10,40,12,38)(13,49,15,51)(14,28,16,26)(17,54,19,56)(21,60,23,58)(22,61,24,63)(25,35,27,33)(34,52,36,50)(41,55,43,53)(45,59,47,57)(46,64,48,62), (1,39,3,37)(2,38,4,40)(5,21,7,23)(6,24,8,22)(9,31,11,29)(10,30,12,32)(13,25,15,27)(14,28,16,26)(17,62,19,64)(18,61,20,63)(33,49,35,51)(34,52,36,50)(41,57,43,59)(42,60,44,58)(45,53,47,55)(46,56,48,54) );
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)], [(1,51,11,25),(2,52,12,26),(3,49,9,27),(4,50,10,28),(5,62,54,58),(6,63,55,59),(7,64,56,60),(8,61,53,57),(13,37,35,31),(14,38,36,32),(15,39,33,29),(16,40,34,30),(17,48,44,23),(18,45,41,24),(19,46,42,21),(20,47,43,22)], [(1,59,11,63),(2,58,12,62),(3,57,9,61),(4,60,10,64),(5,52,54,26),(6,51,55,25),(7,50,56,28),(8,49,53,27),(13,22,35,47),(14,21,36,46),(15,24,33,45),(16,23,34,48),(17,40,44,30),(18,39,41,29),(19,38,42,32),(20,37,43,31)], [(1,37,3,39),(2,32,4,30),(5,42,7,44),(6,20,8,18),(9,29,11,31),(10,40,12,38),(13,49,15,51),(14,28,16,26),(17,54,19,56),(21,60,23,58),(22,61,24,63),(25,35,27,33),(34,52,36,50),(41,55,43,53),(45,59,47,57),(46,64,48,62)], [(1,39,3,37),(2,38,4,40),(5,21,7,23),(6,24,8,22),(9,31,11,29),(10,30,12,32),(13,25,15,27),(14,28,16,26),(17,62,19,64),(18,61,20,63),(33,49,35,51),(34,52,36,50),(41,57,43,59),(42,60,44,58),(45,53,47,55),(46,56,48,54)]])
Matrix representation of C42.73C23 ►in GL8(𝔽17)
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 5 |
| 0 | 0 | 0 | 0 | 5 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 | 0 | 5 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| 0 | 0 | 14 | 14 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 3 | 0 | 0 | 0 | 0 |
| 14 | 14 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 3 | 14 |
| 0 | 0 | 0 | 0 | 0 | 0 | 14 | 14 |
| 0 | 0 | 0 | 0 | 14 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 3 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 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 | 0 | 16 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 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 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 0 | 0 |
G:=sub<GL(8,GF(17))| [0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,0,5,0,0,0,0,0,0,12,0,5,0,0,0,0,5,0,5,0,0,0,0,0,0,5,0,5],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0],[0,0,14,14,0,0,0,0,0,0,14,3,0,0,0,0,14,14,0,0,0,0,0,0,14,3,0,0,0,0,0,0,0,0,0,0,0,0,14,3,0,0,0,0,0,0,3,3,0,0,0,0,3,14,0,0,0,0,0,0,14,14,0,0],[0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,16,0,0,0,0,16,0,0,0,0,0,0,0,0,1,0,0],[0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0] >;
C42.73C23 in GAP, Magma, Sage, TeX
C_4^2._{73}C_2^3 % in TeX
G:=Group("C4^2.73C2^3"); // GroupNames label
G:=SmallGroup(128,2130);
// by ID
G=gap.SmallGroup(128,2130);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,448,253,120,758,723,100,346,80,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=1,c^2=b^2,d^2=e^2=a^2,a*b=b*a,c*a*c^-1=e*a*e^-1=a^-1,d*a*d^-1=a*b^2,c*b*c^-1=d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=b*c,c*e=e*c,d*e=e*d>;
// generators/relations
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