direct product, metacyclic, supersoluble, monomial, A-group
Aliases: C22×C13⋊C3, C26⋊2C6, (C2×C26)⋊3C3, C13⋊2(C2×C6), SmallGroup(156,12)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C22×C13⋊C3 |
Generators and relations for C22×C13⋊C3
G = < a,b,c,d | a2=b2=c13=d3=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c9 >
Character table of C22×C13⋊C3
| class | 1 | 2A | 2B | 2C | 3A | 3B | 6A | 6B | 6C | 6D | 6E | 6F | 13A | 13B | 13C | 13D | 26A | 26B | 26C | 26D | 26E | 26F | 26G | 26H | 26I | 26J | 26K | 26L | |
| size | 1 | 1 | 1 | 1 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
| 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 | 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 | 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 | 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 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ6 | 1 | 1 | -1 | -1 | ζ3 | ζ32 | ζ65 | ζ6 | ζ65 | ζ32 | ζ3 | ζ6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | linear of order 6 |
| ρ7 | 1 | 1 | -1 | -1 | ζ32 | ζ3 | ζ6 | ζ65 | ζ6 | ζ3 | ζ32 | ζ65 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | linear of order 6 |
| ρ8 | 1 | -1 | 1 | -1 | ζ3 | ζ32 | ζ65 | ζ32 | ζ3 | ζ6 | ζ65 | ζ6 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | linear of order 6 |
| ρ9 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ10 | 1 | -1 | 1 | -1 | ζ32 | ζ3 | ζ6 | ζ3 | ζ32 | ζ65 | ζ6 | ζ65 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | linear of order 6 |
| ρ11 | 1 | -1 | -1 | 1 | ζ3 | ζ32 | ζ3 | ζ6 | ζ65 | ζ6 | ζ65 | ζ32 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 6 |
| ρ12 | 1 | -1 | -1 | 1 | ζ32 | ζ3 | ζ32 | ζ65 | ζ6 | ζ65 | ζ6 | ζ3 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 6 |
| ρ13 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | complex lifted from C13⋊C3 |
| ρ14 | 3 | -3 | -3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | -ζ1312-ζ1310-ζ134 | -ζ139-ζ133-ζ13 | complex lifted from C2×C13⋊C3 |
| ρ15 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | complex lifted from C13⋊C3 |
| ρ16 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | complex lifted from C13⋊C3 |
| ρ17 | 3 | 3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ139-ζ133-ζ13 | ζ1312+ζ1310+ζ134 | complex lifted from C2×C13⋊C3 |
| ρ18 | 3 | -3 | 3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | ζ136+ζ135+ζ132 | -ζ1311-ζ138-ζ137 | complex lifted from C2×C13⋊C3 |
| ρ19 | 3 | -3 | -3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | -ζ1311-ζ138-ζ137 | -ζ136-ζ135-ζ132 | complex lifted from C2×C13⋊C3 |
| ρ20 | 3 | -3 | 3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | ζ139+ζ133+ζ13 | -ζ1312-ζ1310-ζ134 | complex lifted from C2×C13⋊C3 |
| ρ21 | 3 | -3 | 3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | ζ1311+ζ138+ζ137 | -ζ136-ζ135-ζ132 | complex lifted from C2×C13⋊C3 |
| ρ22 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | complex lifted from C13⋊C3 |
| ρ23 | 3 | 3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ136-ζ135-ζ132 | ζ1311+ζ138+ζ137 | complex lifted from C2×C13⋊C3 |
| ρ24 | 3 | -3 | -3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | -ζ136-ζ135-ζ132 | -ζ1311-ζ138-ζ137 | complex lifted from C2×C13⋊C3 |
| ρ25 | 3 | 3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ1311-ζ138-ζ137 | ζ136+ζ135+ζ132 | complex lifted from C2×C13⋊C3 |
| ρ26 | 3 | 3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ1312-ζ1310-ζ134 | ζ139+ζ133+ζ13 | complex lifted from C2×C13⋊C3 |
| ρ27 | 3 | -3 | -3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | -ζ139-ζ133-ζ13 | -ζ1312-ζ1310-ζ134 | complex lifted from C2×C13⋊C3 |
| ρ28 | 3 | -3 | 3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | ζ1312+ζ1310+ζ134 | -ζ139-ζ133-ζ13 | complex lifted from C2×C13⋊C3 |
►On 52 points
Generators in S52
(1 27)(2 28)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 41)(16 42)(17 43)(18 44)(19 45)(20 46)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)
(1 14)(2 15)(3 16)(4 17)(5 18)(6 19)(7 20)(8 21)(9 22)(10 23)(11 24)(12 25)(13 26)(27 40)(28 41)(29 42)(30 43)(31 44)(32 45)(33 46)(34 47)(35 48)(36 49)(37 50)(38 51)(39 52)
(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)
(2 4 10)(3 7 6)(5 13 11)(8 9 12)(15 17 23)(16 20 19)(18 26 24)(21 22 25)(28 30 36)(29 33 32)(31 39 37)(34 35 38)(41 43 49)(42 46 45)(44 52 50)(47 48 51)
G:=sub<Sym(52)| (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52), (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52), (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), (2,4,10)(3,7,6)(5,13,11)(8,9,12)(15,17,23)(16,20,19)(18,26,24)(21,22,25)(28,30,36)(29,33,32)(31,39,37)(34,35,38)(41,43,49)(42,46,45)(44,52,50)(47,48,51)>;
G:=Group( (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52), (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52), (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), (2,4,10)(3,7,6)(5,13,11)(8,9,12)(15,17,23)(16,20,19)(18,26,24)(21,22,25)(28,30,36)(29,33,32)(31,39,37)(34,35,38)(41,43,49)(42,46,45)(44,52,50)(47,48,51) );
G=PermutationGroup([[(1,27),(2,28),(3,29),(4,30),(5,31),(6,32),(7,33),(8,34),(9,35),(10,36),(11,37),(12,38),(13,39),(14,40),(15,41),(16,42),(17,43),(18,44),(19,45),(20,46),(21,47),(22,48),(23,49),(24,50),(25,51),(26,52)], [(1,14),(2,15),(3,16),(4,17),(5,18),(6,19),(7,20),(8,21),(9,22),(10,23),(11,24),(12,25),(13,26),(27,40),(28,41),(29,42),(30,43),(31,44),(32,45),(33,46),(34,47),(35,48),(36,49),(37,50),(38,51),(39,52)], [(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)], [(2,4,10),(3,7,6),(5,13,11),(8,9,12),(15,17,23),(16,20,19),(18,26,24),(21,22,25),(28,30,36),(29,33,32),(31,39,37),(34,35,38),(41,43,49),(42,46,45),(44,52,50),(47,48,51)]])
C22×C13⋊C3 is a maximal subgroup of
D26⋊C6
Matrix representation of C22×C13⋊C3 ►in GL4(𝔽79) generated by
| 78 | 0 | 0 | 0 |
| 0 | 78 | 0 | 0 |
| 0 | 0 | 78 | 0 |
| 0 | 0 | 0 | 78 |
| 78 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 50 | 66 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 23 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 12 | 49 | 66 |
| 0 | 40 | 67 | 29 |
G:=sub<GL(4,GF(79))| [78,0,0,0,0,78,0,0,0,0,78,0,0,0,0,78],[78,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,50,1,0,0,66,0,1,0,1,0,0],[23,0,0,0,0,1,12,40,0,0,49,67,0,0,66,29] >;
C22×C13⋊C3 in GAP, Magma, Sage, TeX
C_2^2\times C_{13}\rtimes C_3 % in TeX
G:=Group("C2^2xC13:C3"); // GroupNames label
G:=SmallGroup(156,12);
// by ID
G=gap.SmallGroup(156,12);
# by ID
G:=PCGroup([4,-2,-2,-3,-13,155]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^13=d^3=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^9>;
// generators/relations
Export
Subgroup lattice of C22×C13⋊C3 in TeX
Character table of C22×C13⋊C3 in TeX