direct product, non-abelian, soluble, monomial
Aliases: C2×C2.PSU3(𝔽2), C62.3Q8, C22.3PSU3(𝔽2), C2.2(C2×PSU3(𝔽2)), C32⋊2(C2×C4⋊C4), C3⋊S3⋊2(C4⋊C4), (C3×C6)⋊2(C4⋊C4), (C2×C32⋊C4)⋊5C4, C32⋊C4⋊3(C2×C4), C3⋊S3.8(C2×D4), (C2×C3⋊S3).4Q8, (C3×C6).4(C2×Q8), (C2×C3⋊S3).37D4, C3⋊S3.6(C22×C4), (C2×C3⋊S3).15C23, (C22×C32⋊C4).6C2, (C2×C32⋊C4).20C22, (C22×C3⋊S3).54C22, (C2×C3⋊S3).19(C2×C4), SmallGroup(288,894)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C2.PSU3(𝔽2)
G = < a,b,c,d,e,f | a2=b2=c3=d3=e4=1, f2=be2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, fdf-1=cd=dc, ece-1=d-1, fcf-1=c-1d, ede-1=c, fef-1=be-1 >
Subgroups: 652 in 108 conjugacy classes, 43 normal (13 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, S3, C6, C2×C4, C23, C32, D6, C2×C6, C4⋊C4, C22×C4, C3⋊S3, C3⋊S3, C3×C6, C3×C6, C22×S3, C2×C4⋊C4, C32⋊C4, C32⋊C4, C2×C3⋊S3, C2×C3⋊S3, C62, C2×C32⋊C4, C2×C32⋊C4, C22×C3⋊S3, C2.PSU3(𝔽2), C22×C32⋊C4, C22×C32⋊C4, C2×C2.PSU3(𝔽2)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×C4⋊C4, PSU3(𝔽2), C2.PSU3(𝔽2), C2×PSU3(𝔽2), C2×C2.PSU3(𝔽2)
Character table of C2×C2.PSU3(𝔽2)
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 6A | 6B | 6C | |
| size | 1 | 1 | 1 | 1 | 9 | 9 | 9 | 9 | 8 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 8 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | linear of order 2 |
| ρ9 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | i | -i | i | -i | -1 | 1 | -1 | 1 | -i | i | -i | i | -1 | 1 | -1 | linear of order 4 |
| ρ10 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -i | i | -i | i | -1 | 1 | -1 | 1 | i | -i | i | -i | -1 | 1 | -1 | linear of order 4 |
| ρ11 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | i | -i | -i | i | 1 | -1 | -1 | 1 | i | -i | -i | i | 1 | -1 | -1 | linear of order 4 |
| ρ12 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -i | i | i | -i | 1 | -1 | -1 | 1 | -i | i | i | -i | 1 | -1 | -1 | linear of order 4 |
| ρ13 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | i | i | -i | i | 1 | -1 | 1 | -1 | -i | i | -i | -i | -1 | 1 | -1 | linear of order 4 |
| ρ14 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -i | -i | i | -i | 1 | -1 | 1 | -1 | i | -i | i | i | -1 | 1 | -1 | linear of order 4 |
| ρ15 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | i | i | i | -i | -1 | 1 | 1 | -1 | i | -i | -i | -i | 1 | -1 | -1 | linear of order 4 |
| ρ16 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -i | -i | -i | i | -1 | 1 | 1 | -1 | -i | i | i | i | 1 | -1 | -1 | linear of order 4 |
| ρ17 | 2 | -2 | 2 | -2 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | orthogonal lifted from D4 |
| ρ18 | 2 | -2 | -2 | 2 | -2 | 2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | symplectic lifted from Q8, Schur index 2 |
| ρ20 | 2 | 2 | -2 | -2 | 2 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | symplectic lifted from Q8, Schur index 2 |
| ρ21 | 8 | -8 | -8 | 8 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | orthogonal lifted from C2.PSU3(𝔽2) |
| ρ22 | 8 | 8 | -8 | -8 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | orthogonal lifted from C2×PSU3(𝔽2) |
| ρ23 | 8 | 8 | 8 | 8 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | orthogonal lifted from PSU3(𝔽2) |
| ρ24 | 8 | -8 | 8 | -8 | 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | orthogonal lifted from C2.PSU3(𝔽2) |
►On 48 points
Generators in S48
(1 6)(2 5)(3 11)(4 12)(7 9)(8 10)(13 16)(14 15)(17 25)(18 26)(19 27)(20 28)(21 38)(22 39)(23 40)(24 37)(29 35)(30 36)(31 33)(32 34)(41 46)(42 47)(43 48)(44 45)
(1 12)(2 11)(3 5)(4 6)(7 14)(8 13)(9 15)(10 16)(17 24)(18 21)(19 22)(20 23)(25 37)(26 38)(27 39)(28 40)(29 41)(30 42)(31 43)(32 44)(33 48)(34 45)(35 46)(36 47)
(2 20 18)(3 40 38)(5 28 26)(7 47 45)(8 48 46)(9 42 44)(10 43 41)(11 23 21)(13 33 35)(14 36 34)(15 30 32)(16 31 29)
(1 17 19)(4 37 39)(6 25 27)(7 45 47)(8 48 46)(9 44 42)(10 43 41)(12 24 22)(13 33 35)(14 34 36)(15 32 30)(16 31 29)
(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)
(1 16 12 10)(2 9 11 15)(3 14 5 7)(4 8 6 13)(17 31 22 41)(18 42 23 32)(19 29 24 43)(20 44 21 30)(25 33 39 46)(26 47 40 34)(27 35 37 48)(28 45 38 36)
G:=sub<Sym(48)| (1,6)(2,5)(3,11)(4,12)(7,9)(8,10)(13,16)(14,15)(17,25)(18,26)(19,27)(20,28)(21,38)(22,39)(23,40)(24,37)(29,35)(30,36)(31,33)(32,34)(41,46)(42,47)(43,48)(44,45), (1,12)(2,11)(3,5)(4,6)(7,14)(8,13)(9,15)(10,16)(17,24)(18,21)(19,22)(20,23)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,48)(34,45)(35,46)(36,47), (2,20,18)(3,40,38)(5,28,26)(7,47,45)(8,48,46)(9,42,44)(10,43,41)(11,23,21)(13,33,35)(14,36,34)(15,30,32)(16,31,29), (1,17,19)(4,37,39)(6,25,27)(7,45,47)(8,48,46)(9,44,42)(10,43,41)(12,24,22)(13,33,35)(14,34,36)(15,32,30)(16,31,29), (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), (1,16,12,10)(2,9,11,15)(3,14,5,7)(4,8,6,13)(17,31,22,41)(18,42,23,32)(19,29,24,43)(20,44,21,30)(25,33,39,46)(26,47,40,34)(27,35,37,48)(28,45,38,36)>;
G:=Group( (1,6)(2,5)(3,11)(4,12)(7,9)(8,10)(13,16)(14,15)(17,25)(18,26)(19,27)(20,28)(21,38)(22,39)(23,40)(24,37)(29,35)(30,36)(31,33)(32,34)(41,46)(42,47)(43,48)(44,45), (1,12)(2,11)(3,5)(4,6)(7,14)(8,13)(9,15)(10,16)(17,24)(18,21)(19,22)(20,23)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,48)(34,45)(35,46)(36,47), (2,20,18)(3,40,38)(5,28,26)(7,47,45)(8,48,46)(9,42,44)(10,43,41)(11,23,21)(13,33,35)(14,36,34)(15,30,32)(16,31,29), (1,17,19)(4,37,39)(6,25,27)(7,45,47)(8,48,46)(9,44,42)(10,43,41)(12,24,22)(13,33,35)(14,34,36)(15,32,30)(16,31,29), (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), (1,16,12,10)(2,9,11,15)(3,14,5,7)(4,8,6,13)(17,31,22,41)(18,42,23,32)(19,29,24,43)(20,44,21,30)(25,33,39,46)(26,47,40,34)(27,35,37,48)(28,45,38,36) );
G=PermutationGroup([[(1,6),(2,5),(3,11),(4,12),(7,9),(8,10),(13,16),(14,15),(17,25),(18,26),(19,27),(20,28),(21,38),(22,39),(23,40),(24,37),(29,35),(30,36),(31,33),(32,34),(41,46),(42,47),(43,48),(44,45)], [(1,12),(2,11),(3,5),(4,6),(7,14),(8,13),(9,15),(10,16),(17,24),(18,21),(19,22),(20,23),(25,37),(26,38),(27,39),(28,40),(29,41),(30,42),(31,43),(32,44),(33,48),(34,45),(35,46),(36,47)], [(2,20,18),(3,40,38),(5,28,26),(7,47,45),(8,48,46),(9,42,44),(10,43,41),(11,23,21),(13,33,35),(14,36,34),(15,30,32),(16,31,29)], [(1,17,19),(4,37,39),(6,25,27),(7,45,47),(8,48,46),(9,44,42),(10,43,41),(12,24,22),(13,33,35),(14,34,36),(15,32,30),(16,31,29)], [(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)], [(1,16,12,10),(2,9,11,15),(3,14,5,7),(4,8,6,13),(17,31,22,41),(18,42,23,32),(19,29,24,43),(20,44,21,30),(25,33,39,46),(26,47,40,34),(27,35,37,48),(28,45,38,36)]])
Matrix representation of C2×C2.PSU3(𝔽2) ►in GL10(𝔽13)
| 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 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 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 12 | 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 | 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 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 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 | 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 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
G:=sub<GL(10,GF(13))| [12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0],[5,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0],[0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0] >;
C2×C2.PSU3(𝔽2) in GAP, Magma, Sage, TeX
C_2\times C_2.{\rm PSU}_3({\mathbb F}_2) % in TeX
G:=Group("C2xC2.PSU(3,2)"); // GroupNames label
G:=SmallGroup(288,894);
// by ID
G=gap.SmallGroup(288,894);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,3,56,141,176,9413,2028,362,12550,1581,1203]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^3=d^3=e^4=1,f^2=b*e^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,f*d*f^-1=c*d=d*c,e*c*e^-1=d^-1,f*c*f^-1=c^-1*d,e*d*e^-1=c,f*e*f^-1=b*e^-1>;
// generators/relations
Export