p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.478C23, C4.742+ 1+4, (D4×Q8)⋊9C2, C8⋊D4⋊47C2, C8⋊6D4⋊16C2, C4⋊C4.374D4, C4.Q16⋊36C2, Q8⋊D4⋊24C2, (C4×SD16)⋊58C2, (C2×D4).324D4, C22⋊C4.57D4, D4.D4⋊23C2, C4⋊C4.421C23, C4⋊C8.111C22, (C2×C4).521C24, (C4×C8).293C22, (C2×C8).357C23, Q8.31(C4○D4), C4.SD16⋊34C2, C23.338(C2×D4), C4⋊Q8.156C22, C2.83(D4○SD16), (C2×D4).244C23, (C4×D4).170C22, C4⋊D4.93C22, C4.48(C8.C22), C22⋊C8.89C22, (C4×Q8).166C22, (C2×Q8).400C23, C2.157(D4⋊5D4), C2.D8.125C22, C4.Q8.168C22, C22⋊Q8.92C22, C23.38D4⋊19C2, C23.20D4⋊42C2, (C22×C4).334C23, C22.781(C22×D4), D4⋊C4.208C22, Q8⋊C4.116C22, (C2×SD16).161C22, (C22×Q8).350C22, C42⋊C2.199C22, (C2×M4(2)).123C22, C22.49C24.3C2, C4.246(C2×C4○D4), (C2×C4).614(C2×D4), C2.79(C2×C8.C22), SmallGroup(128,2061)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.478C23
G = < a,b,c,d,e | a4=b4=1, c2=a2, d2=e2=b2, ab=ba, cac-1=a-1, dad-1=ab2, eae-1=a-1b2, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ece-1=a2b2c, ede-1=b2d >
Subgroups: 376 in 193 conjugacy classes, 88 normal (38 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C8, C2×C4, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), SD16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C2×Q8, C4×C8, C22⋊C8, D4⋊C4, Q8⋊C4, Q8⋊C4, C4⋊C8, C4.Q8, C2.D8, C42⋊C2, C42⋊C2, C4×D4, C4×D4, C4×Q8, C4⋊D4, C4⋊D4, C22⋊Q8, C22⋊Q8, C4.4D4, C4⋊Q8, C4⋊Q8, C2×M4(2), C2×SD16, C2×SD16, C22×Q8, C23.38D4, C8⋊6D4, C4×SD16, Q8⋊D4, D4.D4, C8⋊D4, C4.Q16, C23.20D4, C4.SD16, D4×Q8, C22.49C24, C42.478C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, C24, C8.C22, C22×D4, C2×C4○D4, 2+ 1+4, D4⋊5D4, C2×C8.C22, D4○SD16, C42.478C23
Character table of C42.478C23
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 8A | 8B | 8C | 8D | 8E | 8F | |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 8 | 2 | 2 | 2 | 2 | 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 | -2 | 2 | 0 | -2 | -2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | 2 | 2 | 2 | -2 | 0 | -2 | -2 | -2 | -2 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ20 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | -2 | -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 | 0 | 0 | 0 | -2 | 2 | 0 | -2i | 2 | 0 | 0 | 0 | -2 | 2i | 0 | 0 | 0 | 0 | 0 | -2i | 0 | 0 | 2i | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 2i | 2 | 0 | 0 | 0 | -2 | -2i | 0 | 0 | 0 | 0 | 0 | 2i | 0 | 0 | -2i | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 2i | -2 | 0 | 0 | 0 | 2 | -2i | 0 | 0 | 0 | 0 | 0 | -2i | 0 | 0 | 2i | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | -2i | -2 | 0 | 0 | 0 | 2 | 2i | 0 | 0 | 0 | 0 | 0 | 2i | 0 | 0 | -2i | 0 | 0 | complex lifted from C4○D4 |
| ρ25 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | 0 | 4 | -4 | 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 | 0 | 0 | -4 | 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 | 0 | 0 | 4 | 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 | 0 | -2√-2 | 2√-2 | 0 | 0 | 0 | complex lifted from D4○SD16 |
| ρ29 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√-2 | -2√-2 | 0 | 0 | 0 | complex lifted from D4○SD16 |
►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 60 34 23)(2 57 35 24)(3 58 36 21)(4 59 33 22)(5 12 47 26)(6 9 48 27)(7 10 45 28)(8 11 46 25)(13 18 50 53)(14 19 51 54)(15 20 52 55)(16 17 49 56)(29 61 39 44)(30 62 40 41)(31 63 37 42)(32 64 38 43)
(1 49 3 51)(2 52 4 50)(5 40 7 38)(6 39 8 37)(9 61 11 63)(10 64 12 62)(13 35 15 33)(14 34 16 36)(17 58 19 60)(18 57 20 59)(21 54 23 56)(22 53 24 55)(25 42 27 44)(26 41 28 43)(29 46 31 48)(30 45 32 47)
(1 28 34 10)(2 11 35 25)(3 26 36 12)(4 9 33 27)(5 58 47 21)(6 22 48 59)(7 60 45 23)(8 24 46 57)(13 39 50 29)(14 30 51 40)(15 37 52 31)(16 32 49 38)(17 43 56 64)(18 61 53 44)(19 41 54 62)(20 63 55 42)
(1 16 34 49)(2 52 35 15)(3 14 36 51)(4 50 33 13)(5 41 47 62)(6 61 48 44)(7 43 45 64)(8 63 46 42)(9 39 27 29)(10 32 28 38)(11 37 25 31)(12 30 26 40)(17 23 56 60)(18 59 53 22)(19 21 54 58)(20 57 55 24)
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), (1,60,34,23)(2,57,35,24)(3,58,36,21)(4,59,33,22)(5,12,47,26)(6,9,48,27)(7,10,45,28)(8,11,46,25)(13,18,50,53)(14,19,51,54)(15,20,52,55)(16,17,49,56)(29,61,39,44)(30,62,40,41)(31,63,37,42)(32,64,38,43), (1,49,3,51)(2,52,4,50)(5,40,7,38)(6,39,8,37)(9,61,11,63)(10,64,12,62)(13,35,15,33)(14,34,16,36)(17,58,19,60)(18,57,20,59)(21,54,23,56)(22,53,24,55)(25,42,27,44)(26,41,28,43)(29,46,31,48)(30,45,32,47), (1,28,34,10)(2,11,35,25)(3,26,36,12)(4,9,33,27)(5,58,47,21)(6,22,48,59)(7,60,45,23)(8,24,46,57)(13,39,50,29)(14,30,51,40)(15,37,52,31)(16,32,49,38)(17,43,56,64)(18,61,53,44)(19,41,54,62)(20,63,55,42), (1,16,34,49)(2,52,35,15)(3,14,36,51)(4,50,33,13)(5,41,47,62)(6,61,48,44)(7,43,45,64)(8,63,46,42)(9,39,27,29)(10,32,28,38)(11,37,25,31)(12,30,26,40)(17,23,56,60)(18,59,53,22)(19,21,54,58)(20,57,55,24)>;
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), (1,60,34,23)(2,57,35,24)(3,58,36,21)(4,59,33,22)(5,12,47,26)(6,9,48,27)(7,10,45,28)(8,11,46,25)(13,18,50,53)(14,19,51,54)(15,20,52,55)(16,17,49,56)(29,61,39,44)(30,62,40,41)(31,63,37,42)(32,64,38,43), (1,49,3,51)(2,52,4,50)(5,40,7,38)(6,39,8,37)(9,61,11,63)(10,64,12,62)(13,35,15,33)(14,34,16,36)(17,58,19,60)(18,57,20,59)(21,54,23,56)(22,53,24,55)(25,42,27,44)(26,41,28,43)(29,46,31,48)(30,45,32,47), (1,28,34,10)(2,11,35,25)(3,26,36,12)(4,9,33,27)(5,58,47,21)(6,22,48,59)(7,60,45,23)(8,24,46,57)(13,39,50,29)(14,30,51,40)(15,37,52,31)(16,32,49,38)(17,43,56,64)(18,61,53,44)(19,41,54,62)(20,63,55,42), (1,16,34,49)(2,52,35,15)(3,14,36,51)(4,50,33,13)(5,41,47,62)(6,61,48,44)(7,43,45,64)(8,63,46,42)(9,39,27,29)(10,32,28,38)(11,37,25,31)(12,30,26,40)(17,23,56,60)(18,59,53,22)(19,21,54,58)(20,57,55,24) );
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)], [(1,60,34,23),(2,57,35,24),(3,58,36,21),(4,59,33,22),(5,12,47,26),(6,9,48,27),(7,10,45,28),(8,11,46,25),(13,18,50,53),(14,19,51,54),(15,20,52,55),(16,17,49,56),(29,61,39,44),(30,62,40,41),(31,63,37,42),(32,64,38,43)], [(1,49,3,51),(2,52,4,50),(5,40,7,38),(6,39,8,37),(9,61,11,63),(10,64,12,62),(13,35,15,33),(14,34,16,36),(17,58,19,60),(18,57,20,59),(21,54,23,56),(22,53,24,55),(25,42,27,44),(26,41,28,43),(29,46,31,48),(30,45,32,47)], [(1,28,34,10),(2,11,35,25),(3,26,36,12),(4,9,33,27),(5,58,47,21),(6,22,48,59),(7,60,45,23),(8,24,46,57),(13,39,50,29),(14,30,51,40),(15,37,52,31),(16,32,49,38),(17,43,56,64),(18,61,53,44),(19,41,54,62),(20,63,55,42)], [(1,16,34,49),(2,52,35,15),(3,14,36,51),(4,50,33,13),(5,41,47,62),(6,61,48,44),(7,43,45,64),(8,63,46,42),(9,39,27,29),(10,32,28,38),(11,37,25,31),(12,30,26,40),(17,23,56,60),(18,59,53,22),(19,21,54,58),(20,57,55,24)]])
Matrix representation of C42.478C23 ►in GL8(𝔽17)
| 5 | 0 | 3 | 11 | 0 | 0 | 0 | 0 |
| 5 | 12 | 3 | 14 | 0 | 0 | 0 | 0 |
| 3 | 11 | 5 | 0 | 0 | 0 | 0 | 0 |
| 3 | 14 | 5 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 | 0 | 3 |
| 0 | 0 | 0 | 0 | 12 | 0 | 14 | 0 |
| 0 | 0 | 0 | 0 | 0 | 14 | 0 | 12 |
| 0 | 0 | 0 | 0 | 3 | 0 | 5 | 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 | 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 |
| 5 | 7 | 3 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 3 | 0 | 0 | 0 | 0 |
| 14 | 0 | 12 | 10 | 0 | 0 | 0 | 0 |
| 0 | 14 | 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 14 | 0 | 12 |
| 0 | 0 | 0 | 0 | 14 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 | 0 | 3 |
| 0 | 0 | 0 | 0 | 5 | 0 | 3 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 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 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 5 |
| 0 | 0 | 0 | 0 | 0 | 0 | 5 | 5 |
| 12 | 10 | 14 | 0 | 0 | 0 | 0 | 0 |
| 12 | 5 | 14 | 3 | 0 | 0 | 0 | 0 |
| 14 | 0 | 12 | 10 | 0 | 0 | 0 | 0 |
| 14 | 3 | 12 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 14 | 0 | 12 |
| 0 | 0 | 0 | 0 | 3 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 | 0 | 3 |
| 0 | 0 | 0 | 0 | 12 | 0 | 14 | 0 |
G:=sub<GL(8,GF(17))| [5,5,3,3,0,0,0,0,0,12,11,14,0,0,0,0,3,3,5,5,0,0,0,0,11,14,0,12,0,0,0,0,0,0,0,0,0,12,0,3,0,0,0,0,5,0,14,0,0,0,0,0,0,14,0,5,0,0,0,0,3,0,12,0],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0],[5,0,14,0,0,0,0,0,7,12,0,14,0,0,0,0,3,0,12,0,0,0,0,0,0,3,10,5,0,0,0,0,0,0,0,0,0,14,0,5,0,0,0,0,14,0,5,0,0,0,0,0,0,12,0,3,0,0,0,0,12,0,3,0],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,5,0,0,0,0,0,0,5,5,0,0,0,0,0,0,0,0,12,5,0,0,0,0,0,0,5,5],[12,12,14,14,0,0,0,0,10,5,0,3,0,0,0,0,14,14,12,12,0,0,0,0,0,3,10,5,0,0,0,0,0,0,0,0,0,3,0,12,0,0,0,0,14,0,5,0,0,0,0,0,0,5,0,14,0,0,0,0,12,0,3,0] >;
C42.478C23 in GAP, Magma, Sage, TeX
C_4^2._{478}C_2^3 % in TeX
G:=Group("C4^2.478C2^3"); // GroupNames label
G:=SmallGroup(128,2061);
// by ID
G=gap.SmallGroup(128,2061);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,560,253,456,758,723,352,2019,346,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=1,c^2=a^2,d^2=e^2=b^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a*b^2,e*a*e^-1=a^-1*b^2,c*b*c^-1=d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=b*c,e*c*e^-1=a^2*b^2*c,e*d*e^-1=b^2*d>;
// generators/relations
Export