Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13021 |
| 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 | C13×#3414 | 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)(14,15,20,27,21,28,44,59,22,29,19,26,43,58,18,25)(16,30,33,52,34,57,32,62,35,60,42,23,47,50,45,51)(17,36,39,63,40,61,37,24,41,54,38,55,48,53,46,56)(31,65,67,72,68,49,73,74,69,75,70,77,71,76,66,64);(14,16,21,47,22,35,43,34)(15,23,28,62,29,52,58,51)(17,31,48,68,41,69,40,71)(18,42,20,32,44,33,19,45)(24,49,63,75,56,76,55,65)(25,57,27,30,59,50,26,60)(36,72,53,74,54,77,61,64)(37,67,39,73,46,70,38,66);(14,17)(15,24)(16,31)(18,39)(19,37)(20,46)(21,48)(22,41)(23,49)(25,54)(26,53)(27,61)(28,63)(29,56)(30,64)(32,70)(33,66)(34,71)(35,69)(36,59)(38,44)(40,43)(42,73)(45,67)(47,68)(50,72)(51,65)(52,76)(55,58)(57,77)(60,74)(62,75)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6009);