p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.475C23, C4.712+ 1+4, C8⋊D4⋊45C2, C8⋊2D4⋊29C2, C8⋊6D4⋊14C2, C4⋊C4.163D4, Q8.Q8⋊38C2, D4⋊D4⋊48C2, Q8⋊5D4⋊11C2, Q8⋊D4⋊23C2, (C4×SD16)⋊57C2, (C2×D4).177D4, D4.2D4⋊45C2, C4⋊C4.418C23, C4⋊C8.108C22, (C2×C8).104C23, (C2×C4).518C24, (C4×C8).292C22, Q8.28(C4○D4), C22⋊C4.173D4, (C2×D8).87C22, C23.335(C2×D4), C4.Q8.60C22, C2.82(D4○SD16), (C2×D4).242C23, (C4×D4).167C22, C4⋊D4.91C22, C22⋊C8.86C22, (C2×Q8).399C23, (C4×Q8).163C22, C2.154(D4⋊5D4), C2.D8.123C22, C22⋊Q8.89C22, C23.19D4⋊40C2, C23.38D4⋊16C2, C23.36D4⋊23C2, C23.47D4⋊18C2, (C22×C4).331C23, C4.4D4.72C22, C22.778(C22×D4), C42.C2.43C22, D4⋊C4.122C22, C2.92(D8⋊C22), C22.47C24⋊7C2, Q8⋊C4.115C22, (C2×SD16).160C22, (C22×Q8).347C22, C42⋊C2.196C22, C42.78C22⋊22C2, (C2×M4(2)).120C22, C4.243(C2×C4○D4), (C2×C4).929(C2×D4), (C2×C4⋊C4).672C22, (C2×C4○D4).218C22, SmallGroup(128,2058)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.475C23
G = < a,b,c,d,e | a4=b4=e2=1, c2=a2, d2=b2, 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: 400 in 196 conjugacy classes, 86 normal (84 characteristic)
C1, C2, C2, C4, C4, C22, C22, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), D8, SD16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, C4×C8, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊C8, C4.Q8, C2.D8, C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4, C4×Q8, C4⋊D4, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C4.4D4, C4.4D4, C42.C2, C42⋊2C2, C2×M4(2), C2×D8, C2×SD16, C22×Q8, C2×C4○D4, C23.36D4, C23.38D4, C8⋊6D4, C4×SD16, Q8⋊D4, D4⋊D4, D4.2D4, C8⋊D4, C8⋊2D4, Q8.Q8, C23.19D4, C23.47D4, C42.78C22, Q8⋊5D4, C22.47C24, C42.475C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, C24, C22×D4, C2×C4○D4, 2+ 1+4, D4⋊5D4, D8⋊C22, D4○SD16, C42.475C23
Character table of C42.475C23
| 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 | 4 | 4 | 8 | 8 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 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 | 0 | 2 | -2 | -2 | 2 | 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 | 0 | 2 | -2 | -2 | 2 | 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 | 0 | -2 | -2 | -2 | -2 | 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 | 0 | -2 | -2 | -2 | -2 | 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 | 0 | 2 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | -2i | 2i | 0 | 0 | 0 | 0 | 0 | -2i | 0 | 2i | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | -2i | 2i | 0 | 0 | 0 | 0 | 0 | 2i | 0 | -2i | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 2i | -2i | 0 | 0 | 0 | 0 | 0 | 2i | 0 | -2i | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | 2i | -2i | 0 | 0 | 0 | 0 | 0 | -2i | 0 | 2i | 0 | 0 | complex lifted from C4○D4 |
| ρ25 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | -4 | 4 | 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 | 0 | 4i | 0 | 0 | -4i | 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 | 0 | -4i | 0 | 0 | 4i | 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 | -2√-2 | 0 | 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 | 2√-2 | 0 | -2√-2 | 0 | 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 9 51 41)(2 10 52 42)(3 11 49 43)(4 12 50 44)(5 36 56 27)(6 33 53 28)(7 34 54 25)(8 35 55 26)(13 21 47 17)(14 22 48 18)(15 23 45 19)(16 24 46 20)(29 62 58 38)(30 63 59 39)(31 64 60 40)(32 61 57 37)
(1 8 3 6)(2 54 4 56)(5 52 7 50)(9 26 11 28)(10 34 12 36)(13 32 15 30)(14 60 16 58)(17 61 19 63)(18 40 20 38)(21 37 23 39)(22 64 24 62)(25 44 27 42)(29 48 31 46)(33 41 35 43)(45 59 47 57)(49 53 51 55)
(1 24 51 20)(2 17 52 21)(3 22 49 18)(4 19 50 23)(5 59 56 30)(6 31 53 60)(7 57 54 32)(8 29 55 58)(9 16 41 46)(10 47 42 13)(11 14 43 48)(12 45 44 15)(25 37 34 61)(26 62 35 38)(27 39 36 63)(28 64 33 40)
(1 20)(2 19)(3 18)(4 17)(5 39)(6 38)(7 37)(8 40)(9 16)(10 15)(11 14)(12 13)(21 50)(22 49)(23 52)(24 51)(25 57)(26 60)(27 59)(28 58)(29 33)(30 36)(31 35)(32 34)(41 46)(42 45)(43 48)(44 47)(53 62)(54 61)(55 64)(56 63)
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), (1,9,51,41)(2,10,52,42)(3,11,49,43)(4,12,50,44)(5,36,56,27)(6,33,53,28)(7,34,54,25)(8,35,55,26)(13,21,47,17)(14,22,48,18)(15,23,45,19)(16,24,46,20)(29,62,58,38)(30,63,59,39)(31,64,60,40)(32,61,57,37), (1,8,3,6)(2,54,4,56)(5,52,7,50)(9,26,11,28)(10,34,12,36)(13,32,15,30)(14,60,16,58)(17,61,19,63)(18,40,20,38)(21,37,23,39)(22,64,24,62)(25,44,27,42)(29,48,31,46)(33,41,35,43)(45,59,47,57)(49,53,51,55), (1,24,51,20)(2,17,52,21)(3,22,49,18)(4,19,50,23)(5,59,56,30)(6,31,53,60)(7,57,54,32)(8,29,55,58)(9,16,41,46)(10,47,42,13)(11,14,43,48)(12,45,44,15)(25,37,34,61)(26,62,35,38)(27,39,36,63)(28,64,33,40), (1,20)(2,19)(3,18)(4,17)(5,39)(6,38)(7,37)(8,40)(9,16)(10,15)(11,14)(12,13)(21,50)(22,49)(23,52)(24,51)(25,57)(26,60)(27,59)(28,58)(29,33)(30,36)(31,35)(32,34)(41,46)(42,45)(43,48)(44,47)(53,62)(54,61)(55,64)(56,63)>;
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), (1,9,51,41)(2,10,52,42)(3,11,49,43)(4,12,50,44)(5,36,56,27)(6,33,53,28)(7,34,54,25)(8,35,55,26)(13,21,47,17)(14,22,48,18)(15,23,45,19)(16,24,46,20)(29,62,58,38)(30,63,59,39)(31,64,60,40)(32,61,57,37), (1,8,3,6)(2,54,4,56)(5,52,7,50)(9,26,11,28)(10,34,12,36)(13,32,15,30)(14,60,16,58)(17,61,19,63)(18,40,20,38)(21,37,23,39)(22,64,24,62)(25,44,27,42)(29,48,31,46)(33,41,35,43)(45,59,47,57)(49,53,51,55), (1,24,51,20)(2,17,52,21)(3,22,49,18)(4,19,50,23)(5,59,56,30)(6,31,53,60)(7,57,54,32)(8,29,55,58)(9,16,41,46)(10,47,42,13)(11,14,43,48)(12,45,44,15)(25,37,34,61)(26,62,35,38)(27,39,36,63)(28,64,33,40), (1,20)(2,19)(3,18)(4,17)(5,39)(6,38)(7,37)(8,40)(9,16)(10,15)(11,14)(12,13)(21,50)(22,49)(23,52)(24,51)(25,57)(26,60)(27,59)(28,58)(29,33)(30,36)(31,35)(32,34)(41,46)(42,45)(43,48)(44,47)(53,62)(54,61)(55,64)(56,63) );
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)], [(1,9,51,41),(2,10,52,42),(3,11,49,43),(4,12,50,44),(5,36,56,27),(6,33,53,28),(7,34,54,25),(8,35,55,26),(13,21,47,17),(14,22,48,18),(15,23,45,19),(16,24,46,20),(29,62,58,38),(30,63,59,39),(31,64,60,40),(32,61,57,37)], [(1,8,3,6),(2,54,4,56),(5,52,7,50),(9,26,11,28),(10,34,12,36),(13,32,15,30),(14,60,16,58),(17,61,19,63),(18,40,20,38),(21,37,23,39),(22,64,24,62),(25,44,27,42),(29,48,31,46),(33,41,35,43),(45,59,47,57),(49,53,51,55)], [(1,24,51,20),(2,17,52,21),(3,22,49,18),(4,19,50,23),(5,59,56,30),(6,31,53,60),(7,57,54,32),(8,29,55,58),(9,16,41,46),(10,47,42,13),(11,14,43,48),(12,45,44,15),(25,37,34,61),(26,62,35,38),(27,39,36,63),(28,64,33,40)], [(1,20),(2,19),(3,18),(4,17),(5,39),(6,38),(7,37),(8,40),(9,16),(10,15),(11,14),(12,13),(21,50),(22,49),(23,52),(24,51),(25,57),(26,60),(27,59),(28,58),(29,33),(30,36),(31,35),(32,34),(41,46),(42,45),(43,48),(44,47),(53,62),(54,61),(55,64),(56,63)]])
Matrix representation of C42.475C23 ►in GL8(𝔽17)
| 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 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 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 |
| 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 | 5 | 12 | 13 | 4 |
| 0 | 0 | 0 | 0 | 12 | 12 | 4 | 4 |
| 0 | 0 | 0 | 0 | 4 | 13 | 12 | 5 |
| 0 | 0 | 0 | 0 | 13 | 13 | 5 | 5 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 0 | 0 | 0 |
G:=sub<GL(8,GF(17))| [0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,4,0],[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],[0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,12,4,13,0,0,0,0,12,12,13,13,0,0,0,0,13,4,12,5,0,0,0,0,4,4,5,5],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0],[16,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,4,0,0,0,0,0,0,13,0,0,0,0,0,0,4,0,0,0] >;
C42.475C23 in GAP, Magma, Sage, TeX
C_4^2._{475}C_2^3 % in TeX
G:=Group("C4^2.475C2^3"); // GroupNames label
G:=SmallGroup(128,2058);
// by ID
G=gap.SmallGroup(128,2058);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,112,253,758,723,352,2019,346,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=e^2=1,c^2=a^2,d^2=b^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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