Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13016 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1879 |
| prime radical | C2×C13×#508 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,26,21,27,43,59,22,28,19,44,42,58,18,25)(16,29,33,52,34,57,31,60,35,63,32,23,47,50,45,51)(17,36,38,61,39,72,37,24,40,54,41,55,48,53,46,56)(30,64,66,71,67,49,69,62,68,75,73,77,70,76,65,74);(14,16,21,47,22,35,42,34)(15,23,27,60,28,52,58,51)(17,30,48,67,40,68,39,70)(18,32,20,31,43,33,19,45)(24,49,61,75,56,76,55,64)(25,57,26,29,59,50,44,63)(36,71,53,62,54,77,72,74)(37,66,38,69,46,73,41,65);(14,17)(15,24)(16,30)(18,41)(19,46)(20,37)(21,48)(22,40)(23,49)(25,36)(26,53)(27,61)(28,56)(29,62)(31,66)(32,65)(33,69)(34,70)(35,68)(38,43)(39,42)(44,72)(45,73)(47,67)(50,77)(51,64)(52,76)(54,59)(55,58)(57,71)(60,75)(63,74)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6004);