p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.51C23, C4.612+ 1+4, C8⋊9D4⋊18C2, C8⋊8D4⋊51C2, C4⋊C4.158D4, D4⋊3Q8⋊4C2, Q8⋊Q8⋊17C2, (C2×D4).318D4, C8.D4⋊26C2, (C2×C8).99C23, Q8⋊5D4.4C2, Q16⋊C4⋊23C2, D4.7D4⋊46C2, C4⋊C8.104C22, C4⋊C4.236C23, (C2×C4).508C24, Q8.24(C4○D4), Q8.D4⋊43C2, C22⋊Q16⋊32C2, C22⋊C4.168D4, C23.476(C2×D4), C4⋊Q8.152C22, C8⋊C4.45C22, C4.Q8.58C22, C2.76(D4○SD16), (C2×D4).234C23, (C4×D4).161C22, C4⋊D4.85C22, C22⋊C8.82C22, (C2×Q8).221C23, (C4×Q8).159C22, (C2×Q16).85C22, C2.144(D4⋊5D4), C22⋊Q8.83C22, D4⋊C4.73C22, C23.47D4⋊17C2, C23.46D4⋊15C2, C23.36D4⋊19C2, (C22×C8).363C22, Q8⋊C4.72C22, C4.4D4.67C22, C22.768(C22×D4), C22.7(C8.C22), (C22×C4).1152C23, (C2×SD16).100C22, (C22×Q8).344C22, C42.28C22⋊17C2, (C2×M4(2)).115C22, C4.233(C2×C4○D4), (C2×C4).605(C2×D4), (C2×Q8⋊C4)⋊43C2, C2.76(C2×C8.C22), (C2×C4⋊C4).669C22, (C2×C4○D4).212C22, SmallGroup(128,2048)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.51C23
G = < a,b,c,d,e | a4=b4=e2=1, c2=a2b2, d2=b2, ab=ba, cac-1=eae=a-1, dad-1=ab2, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ece=a2c, ede=b2d >
Subgroups: 376 in 194 conjugacy classes, 88 normal (84 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), SD16, Q16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, C8⋊C4, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊C8, C4.Q8, C2×C4⋊C4, C4×D4, C4×D4, C4×Q8, C4⋊D4, C4⋊D4, C22⋊Q8, C22⋊Q8, C4.4D4, C4.4D4, C42.C2, C4⋊Q8, C22×C8, C2×M4(2), C2×SD16, C2×Q16, C22×Q8, C2×C4○D4, C2×Q8⋊C4, C23.36D4, C8⋊9D4, Q16⋊C4, C22⋊Q16, D4.7D4, Q8.D4, C8⋊8D4, C8.D4, Q8⋊Q8, C23.46D4, C23.47D4, C42.28C22, Q8⋊5D4, D4⋊3Q8, C42.51C23
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, C42.51C23
Character table of C42.51C23
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 8A | 8B | 8C | 8D | 8E | 8F | |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 8 | 2 | 2 | 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 | -2 | -2 | -2 | 0 | -2 | -2 | 0 | 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 | 2 | 2 | 2 | 0 | -2 | -2 | 0 | 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 | 2 | 2 | -2 | 0 | -2 | -2 | 0 | -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 | -2 | -2 | 2 | 0 | -2 | -2 | 0 | -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 | 0 | 0 | 0 | 2 | -2 | -2i | 0 | 0 | 2 | 0 | 0 | 2i | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2i | 2i | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 2i | 0 | 0 | -2 | 0 | 0 | -2i | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2i | 2i | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 2i | 0 | 0 | 2 | 0 | 0 | -2i | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2i | -2i | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2i | 0 | 0 | -2 | 0 | 0 | 2i | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2i | -2i | 0 | 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 | 4 | -4 | 0 | 0 | 0 | 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 | -4 | 4 | 0 | 0 | 0 | 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 | 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 | 2√-2 | 0 | 0 | -2√-2 | 0 | 0 | complex lifted from D4○SD16 |
►On 64 points
(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 48 17 44)(2 45 18 41)(3 46 19 42)(4 47 20 43)(5 36 40 62)(6 33 37 63)(7 34 38 64)(8 35 39 61)(9 52 22 14)(10 49 23 15)(11 50 24 16)(12 51 21 13)(25 54 59 31)(26 55 60 32)(27 56 57 29)(28 53 58 30)
(1 55 19 30)(2 54 20 29)(3 53 17 32)(4 56 18 31)(5 52 38 16)(6 51 39 15)(7 50 40 14)(8 49 37 13)(9 64 24 36)(10 63 21 35)(11 62 22 34)(12 61 23 33)(25 43 57 45)(26 42 58 48)(27 41 59 47)(28 44 60 46)
(1 11 17 24)(2 21 18 12)(3 9 19 22)(4 23 20 10)(5 55 40 32)(6 29 37 56)(7 53 38 30)(8 31 39 54)(13 45 51 41)(14 42 52 46)(15 47 49 43)(16 44 50 48)(25 35 59 61)(26 62 60 36)(27 33 57 63)(28 64 58 34)
(1 24)(2 23)(3 22)(4 21)(5 28)(6 27)(7 26)(8 25)(9 19)(10 18)(11 17)(12 20)(13 47)(14 46)(15 45)(16 48)(29 63)(30 62)(31 61)(32 64)(33 56)(34 55)(35 54)(36 53)(37 57)(38 60)(39 59)(40 58)(41 49)(42 52)(43 51)(44 50)
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), (1,48,17,44)(2,45,18,41)(3,46,19,42)(4,47,20,43)(5,36,40,62)(6,33,37,63)(7,34,38,64)(8,35,39,61)(9,52,22,14)(10,49,23,15)(11,50,24,16)(12,51,21,13)(25,54,59,31)(26,55,60,32)(27,56,57,29)(28,53,58,30), (1,55,19,30)(2,54,20,29)(3,53,17,32)(4,56,18,31)(5,52,38,16)(6,51,39,15)(7,50,40,14)(8,49,37,13)(9,64,24,36)(10,63,21,35)(11,62,22,34)(12,61,23,33)(25,43,57,45)(26,42,58,48)(27,41,59,47)(28,44,60,46), (1,11,17,24)(2,21,18,12)(3,9,19,22)(4,23,20,10)(5,55,40,32)(6,29,37,56)(7,53,38,30)(8,31,39,54)(13,45,51,41)(14,42,52,46)(15,47,49,43)(16,44,50,48)(25,35,59,61)(26,62,60,36)(27,33,57,63)(28,64,58,34), (1,24)(2,23)(3,22)(4,21)(5,28)(6,27)(7,26)(8,25)(9,19)(10,18)(11,17)(12,20)(13,47)(14,46)(15,45)(16,48)(29,63)(30,62)(31,61)(32,64)(33,56)(34,55)(35,54)(36,53)(37,57)(38,60)(39,59)(40,58)(41,49)(42,52)(43,51)(44,50)>;
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), (1,48,17,44)(2,45,18,41)(3,46,19,42)(4,47,20,43)(5,36,40,62)(6,33,37,63)(7,34,38,64)(8,35,39,61)(9,52,22,14)(10,49,23,15)(11,50,24,16)(12,51,21,13)(25,54,59,31)(26,55,60,32)(27,56,57,29)(28,53,58,30), (1,55,19,30)(2,54,20,29)(3,53,17,32)(4,56,18,31)(5,52,38,16)(6,51,39,15)(7,50,40,14)(8,49,37,13)(9,64,24,36)(10,63,21,35)(11,62,22,34)(12,61,23,33)(25,43,57,45)(26,42,58,48)(27,41,59,47)(28,44,60,46), (1,11,17,24)(2,21,18,12)(3,9,19,22)(4,23,20,10)(5,55,40,32)(6,29,37,56)(7,53,38,30)(8,31,39,54)(13,45,51,41)(14,42,52,46)(15,47,49,43)(16,44,50,48)(25,35,59,61)(26,62,60,36)(27,33,57,63)(28,64,58,34), (1,24)(2,23)(3,22)(4,21)(5,28)(6,27)(7,26)(8,25)(9,19)(10,18)(11,17)(12,20)(13,47)(14,46)(15,45)(16,48)(29,63)(30,62)(31,61)(32,64)(33,56)(34,55)(35,54)(36,53)(37,57)(38,60)(39,59)(40,58)(41,49)(42,52)(43,51)(44,50) );
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)], [(1,48,17,44),(2,45,18,41),(3,46,19,42),(4,47,20,43),(5,36,40,62),(6,33,37,63),(7,34,38,64),(8,35,39,61),(9,52,22,14),(10,49,23,15),(11,50,24,16),(12,51,21,13),(25,54,59,31),(26,55,60,32),(27,56,57,29),(28,53,58,30)], [(1,55,19,30),(2,54,20,29),(3,53,17,32),(4,56,18,31),(5,52,38,16),(6,51,39,15),(7,50,40,14),(8,49,37,13),(9,64,24,36),(10,63,21,35),(11,62,22,34),(12,61,23,33),(25,43,57,45),(26,42,58,48),(27,41,59,47),(28,44,60,46)], [(1,11,17,24),(2,21,18,12),(3,9,19,22),(4,23,20,10),(5,55,40,32),(6,29,37,56),(7,53,38,30),(8,31,39,54),(13,45,51,41),(14,42,52,46),(15,47,49,43),(16,44,50,48),(25,35,59,61),(26,62,60,36),(27,33,57,63),(28,64,58,34)], [(1,24),(2,23),(3,22),(4,21),(5,28),(6,27),(7,26),(8,25),(9,19),(10,18),(11,17),(12,20),(13,47),(14,46),(15,45),(16,48),(29,63),(30,62),(31,61),(32,64),(33,56),(34,55),(35,54),(36,53),(37,57),(38,60),(39,59),(40,58),(41,49),(42,52),(43,51),(44,50)]])
Matrix representation of C42.51C23 ►in GL8(𝔽17)
| 16 | 1 | 16 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 0 | 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 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 | 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 | 16 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 16 | 1 | 15 | 0 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 2 | 15 | 2 |
| 0 | 0 | 0 | 0 | 2 | 2 | 15 | 15 |
| 0 | 0 | 0 | 0 | 15 | 15 | 15 | 15 |
| 0 | 0 | 0 | 0 | 2 | 15 | 15 | 2 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 16 | 1 | 15 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 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 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 16 | 1 | 16 | 2 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 0 | 0 |
G:=sub<GL(8,GF(17))| [16,0,0,16,0,0,0,0,1,0,16,0,0,0,0,0,16,1,0,16,0,0,0,0,2,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,16,0,0],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,16,0],[0,1,16,16,0,0,0,0,0,16,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,15,0,1,0,0,0,0,0,0,0,0,15,2,15,2,0,0,0,0,2,2,15,15,0,0,0,0,15,15,15,15,0,0,0,0,2,15,15,2],[0,1,1,0,0,0,0,0,0,16,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,15,0,1,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[0,16,1,1,0,0,0,0,0,1,0,0,0,0,0,0,1,16,0,1,0,0,0,0,0,2,0,16,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,16,0,0] >;
C42.51C23 in GAP, Magma, Sage, TeX
C_4^2._{51}C_2^3 % in TeX
G:=Group("C4^2.51C2^3"); // GroupNames label
G:=SmallGroup(128,2048);
// by ID
G=gap.SmallGroup(128,2048);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,560,253,758,723,352,346,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=e^2=1,c^2=a^2*b^2,d^2=b^2,a*b=b*a,c*a*c^-1=e*a*e=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,e*c*e=a^2*c,e*d*e=b^2*d>;
// generators/relations
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