p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.492C23, C4.862- 1+4, C8⋊D4⋊54C2, C8⋊6D4⋊21C2, C4⋊C4.169D4, D4.Q8⋊44C2, Q8.Q8⋊44C2, (C4×SD16)⋊22C2, (C2×D4).183D4, C8.15(C4○D4), C8.5Q8⋊21C2, C4⋊C4.256C23, C4⋊C8.124C22, (C4×C8).193C22, (C2×C8).366C23, (C2×C4).543C24, C22⋊C4.179D4, C23.348(C2×D4), C2.96(D4⋊6D4), C2.93(D4○SD16), (C4×D4).183C22, (C2×D4).260C23, (C4×Q8).182C22, (C2×Q8).245C23, M4(2)⋊C4⋊38C2, C4.Q8.111C22, C2.D8.133C22, C23.20D4⋊48C2, C4⋊D4.109C22, C23.46D4⋊23C2, C23.19D4⋊47C2, C23.47D4⋊23C2, C22⋊C8.102C22, (C22×C4).343C23, Q8⋊C4.82C22, C22.803(C22×D4), C22⋊Q8.108C22, C42.C2.56C22, D4⋊C4.188C22, C2.98(D8⋊C22), (C2×SD16).120C22, C42⋊C2.214C22, C22.46C24⋊11C2, (C2×M4(2)).136C22, C22.47C24.5C2, C4.125(C2×C4○D4), (C2×C4).627(C2×D4), (C2×C4⋊C4).692C22, SmallGroup(128,2083)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.492C23
G = < a,b,c,d,e | a4=b4=e2=1, c2=d2=a2, ab=ba, cac-1=a-1b2, dad-1=ab2, eae=a-1, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ece=a2c, ede=b2d >
Subgroups: 320 in 174 conjugacy classes, 86 normal (84 characteristic)
C1, C2, C2, C4, C4, C22, C22, C8, C8, C2×C4, C2×C4, D4, Q8, C23, C23, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), SD16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4×C8, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊C8, C4.Q8, C2.D8, C2×C4⋊C4, C42⋊C2, C42⋊C2, C4×D4, C4×D4, C4×Q8, C4⋊D4, C4⋊D4, C22⋊Q8, C22.D4, C42.C2, C42.C2, C42⋊2C2, C2×M4(2), C2×SD16, M4(2)⋊C4, C8⋊6D4, C4×SD16, C8⋊D4, D4.Q8, Q8.Q8, C23.46D4, C23.19D4, C23.47D4, C23.20D4, C8.5Q8, C22.46C24, C22.47C24, C42.492C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, C24, C22×D4, C2×C4○D4, 2- 1+4, D4⋊6D4, D8⋊C22, D4○SD16, C42.492C23
Character table of C42.492C23
| 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 | 0 | 2 | 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 | 0 | -2 | 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 | 0 | -2 | 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 | 0 | 2 | 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 | -2i | 0 | 0 | 2i | 0 | 2i | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | -2i | 2i | 0 | 0 | -2i | 0 | 2i | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 2i | 2i | 0 | 0 | -2i | 0 | -2i | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 2i | -2i | 0 | 0 | 2i | 0 | -2i | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 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 | symplectic lifted from 2- 1+4, Schur index 2 |
| ρ26 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | 4i | 0 | 0 | -4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D8⋊C22 |
| ρ27 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | -4i | 0 | 0 | 4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D8⋊C22 |
| 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 23 39 33)(2 24 40 34)(3 21 37 35)(4 22 38 36)(5 62 30 26)(6 63 31 27)(7 64 32 28)(8 61 29 25)(9 13 53 59)(10 14 54 60)(11 15 55 57)(12 16 56 58)(17 46 44 51)(18 47 41 52)(19 48 42 49)(20 45 43 50)
(1 56 3 54)(2 11 4 9)(5 42 7 44)(6 18 8 20)(10 39 12 37)(13 34 15 36)(14 23 16 21)(17 30 19 32)(22 59 24 57)(25 45 27 47)(26 49 28 51)(29 43 31 41)(33 58 35 60)(38 53 40 55)(46 62 48 64)(50 63 52 61)
(1 44 3 42)(2 18 4 20)(5 14 7 16)(6 57 8 59)(9 27 11 25)(10 64 12 62)(13 31 15 29)(17 37 19 39)(21 48 23 46)(22 50 24 52)(26 54 28 56)(30 60 32 58)(33 51 35 49)(34 47 36 45)(38 43 40 41)(53 63 55 61)
(1 56)(2 55)(3 54)(4 53)(5 46)(6 45)(7 48)(8 47)(9 38)(10 37)(11 40)(12 39)(13 36)(14 35)(15 34)(16 33)(17 26)(18 25)(19 28)(20 27)(21 60)(22 59)(23 58)(24 57)(29 52)(30 51)(31 50)(32 49)(41 61)(42 64)(43 63)(44 62)
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), (1,23,39,33)(2,24,40,34)(3,21,37,35)(4,22,38,36)(5,62,30,26)(6,63,31,27)(7,64,32,28)(8,61,29,25)(9,13,53,59)(10,14,54,60)(11,15,55,57)(12,16,56,58)(17,46,44,51)(18,47,41,52)(19,48,42,49)(20,45,43,50), (1,56,3,54)(2,11,4,9)(5,42,7,44)(6,18,8,20)(10,39,12,37)(13,34,15,36)(14,23,16,21)(17,30,19,32)(22,59,24,57)(25,45,27,47)(26,49,28,51)(29,43,31,41)(33,58,35,60)(38,53,40,55)(46,62,48,64)(50,63,52,61), (1,44,3,42)(2,18,4,20)(5,14,7,16)(6,57,8,59)(9,27,11,25)(10,64,12,62)(13,31,15,29)(17,37,19,39)(21,48,23,46)(22,50,24,52)(26,54,28,56)(30,60,32,58)(33,51,35,49)(34,47,36,45)(38,43,40,41)(53,63,55,61), (1,56)(2,55)(3,54)(4,53)(5,46)(6,45)(7,48)(8,47)(9,38)(10,37)(11,40)(12,39)(13,36)(14,35)(15,34)(16,33)(17,26)(18,25)(19,28)(20,27)(21,60)(22,59)(23,58)(24,57)(29,52)(30,51)(31,50)(32,49)(41,61)(42,64)(43,63)(44,62)>;
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), (1,23,39,33)(2,24,40,34)(3,21,37,35)(4,22,38,36)(5,62,30,26)(6,63,31,27)(7,64,32,28)(8,61,29,25)(9,13,53,59)(10,14,54,60)(11,15,55,57)(12,16,56,58)(17,46,44,51)(18,47,41,52)(19,48,42,49)(20,45,43,50), (1,56,3,54)(2,11,4,9)(5,42,7,44)(6,18,8,20)(10,39,12,37)(13,34,15,36)(14,23,16,21)(17,30,19,32)(22,59,24,57)(25,45,27,47)(26,49,28,51)(29,43,31,41)(33,58,35,60)(38,53,40,55)(46,62,48,64)(50,63,52,61), (1,44,3,42)(2,18,4,20)(5,14,7,16)(6,57,8,59)(9,27,11,25)(10,64,12,62)(13,31,15,29)(17,37,19,39)(21,48,23,46)(22,50,24,52)(26,54,28,56)(30,60,32,58)(33,51,35,49)(34,47,36,45)(38,43,40,41)(53,63,55,61), (1,56)(2,55)(3,54)(4,53)(5,46)(6,45)(7,48)(8,47)(9,38)(10,37)(11,40)(12,39)(13,36)(14,35)(15,34)(16,33)(17,26)(18,25)(19,28)(20,27)(21,60)(22,59)(23,58)(24,57)(29,52)(30,51)(31,50)(32,49)(41,61)(42,64)(43,63)(44,62) );
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)], [(1,23,39,33),(2,24,40,34),(3,21,37,35),(4,22,38,36),(5,62,30,26),(6,63,31,27),(7,64,32,28),(8,61,29,25),(9,13,53,59),(10,14,54,60),(11,15,55,57),(12,16,56,58),(17,46,44,51),(18,47,41,52),(19,48,42,49),(20,45,43,50)], [(1,56,3,54),(2,11,4,9),(5,42,7,44),(6,18,8,20),(10,39,12,37),(13,34,15,36),(14,23,16,21),(17,30,19,32),(22,59,24,57),(25,45,27,47),(26,49,28,51),(29,43,31,41),(33,58,35,60),(38,53,40,55),(46,62,48,64),(50,63,52,61)], [(1,44,3,42),(2,18,4,20),(5,14,7,16),(6,57,8,59),(9,27,11,25),(10,64,12,62),(13,31,15,29),(17,37,19,39),(21,48,23,46),(22,50,24,52),(26,54,28,56),(30,60,32,58),(33,51,35,49),(34,47,36,45),(38,43,40,41),(53,63,55,61)], [(1,56),(2,55),(3,54),(4,53),(5,46),(6,45),(7,48),(8,47),(9,38),(10,37),(11,40),(12,39),(13,36),(14,35),(15,34),(16,33),(17,26),(18,25),(19,28),(20,27),(21,60),(22,59),(23,58),(24,57),(29,52),(30,51),(31,50),(32,49),(41,61),(42,64),(43,63),(44,62)]])
Matrix representation of C42.492C23 ►in GL8(𝔽17)
| 7 | 0 | 0 | 10 | 0 | 0 | 0 | 0 |
| 10 | 5 | 5 | 12 | 0 | 0 | 0 | 0 |
| 5 | 5 | 12 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 | 0 | 16 |
| 0 | 0 | 0 | 0 | 6 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 6 |
| 0 | 0 | 0 | 0 | 16 | 0 | 11 | 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 |
| 10 | 10 | 10 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 12 | 12 | 0 | 0 | 0 | 0 |
| 12 | 12 | 12 | 5 | 0 | 0 | 0 | 0 |
| 5 | 0 | 10 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 0 | 11 |
| 0 | 0 | 0 | 0 | 16 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 6 | 0 | 1 |
| 0 | 0 | 0 | 0 | 6 | 0 | 1 | 0 |
| 16 | 0 | 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 16 | 16 | 16 | 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 |
| 7 | 7 | 7 | 0 | 0 | 0 | 0 | 0 |
| 10 | 5 | 5 | 12 | 0 | 0 | 0 | 0 |
| 5 | 5 | 5 | 5 | 0 | 0 | 0 | 0 |
| 12 | 0 | 7 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 6 |
| 0 | 0 | 0 | 0 | 16 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 | 0 | 16 |
| 0 | 0 | 0 | 0 | 6 | 0 | 1 | 0 |
G:=sub<GL(8,GF(17))| [7,10,5,12,0,0,0,0,0,5,5,0,0,0,0,0,0,5,12,0,0,0,0,0,10,12,12,10,0,0,0,0,0,0,0,0,0,6,0,16,0,0,0,0,11,0,1,0,0,0,0,0,0,1,0,11,0,0,0,0,16,0,6,0],[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],[10,0,12,5,0,0,0,0,10,12,12,0,0,0,0,0,10,12,12,10,0,0,0,0,0,12,5,0,0,0,0,0,0,0,0,0,0,16,0,6,0,0,0,0,16,0,6,0,0,0,0,0,0,11,0,1,0,0,0,0,11,0,1,0],[16,0,1,16,0,0,0,0,0,0,0,16,0,0,0,0,15,1,1,16,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,5,0,0,0,0,0,0,5,5,0,0,0,0,0,0,0,0,12,5,0,0,0,0,0,0,5,5],[7,10,5,12,0,0,0,0,7,5,5,0,0,0,0,0,7,5,5,7,0,0,0,0,0,12,5,0,0,0,0,0,0,0,0,0,0,16,0,6,0,0,0,0,1,0,11,0,0,0,0,0,0,11,0,1,0,0,0,0,6,0,16,0] >;
C42.492C23 in GAP, Magma, Sage, TeX
C_4^2._{492}C_2^3 % in TeX
G:=Group("C4^2.492C2^3"); // GroupNames label
G:=SmallGroup(128,2083);
// by ID
G=gap.SmallGroup(128,2083);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,112,253,758,723,100,2019,346,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=e^2=1,c^2=d^2=a^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a*b^2,e*a*e=a^-1,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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