Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,22,23,19)(17,25,26,20)(24,27,29,28)(30,31)(32,36)(33,43)(34,46)(35,38)(37,44)(39,48)(40,54)(41,50)(42,58)(45,53)(47,52)(49,56)(51,57)(55,61)(59,60);(14,16)(15,19)(17,24)(18,23)(20,27)(21,22)(25,28)(26,29)(30,32)(31,36)(33,40)(34,42)(35,41)(37,49)(38,50)(39,51)(43,54)(44,56)(45,55)(46,58)(47,59)(48,57)(52,60)(53,61);(30,33,35,45)(31,37,38,52)(32,40,41,55)(34,47,48,44)(36,49,50,60)(39,53,46,43)(42,59,57,56)(51,61,58,54);(16,23)(19,22)(24,29)(27,28)(31,38)(36,50)(37,52)(39,46)(43,53)(49,60)(51,58)(54,61);(14,17,18,26)(15,20,21,25)(16,24,23,29)(19,27,22,28)(32,41)(36,50)(40,55)(42,57)(49,60)(51,58)(54,61)(56,59)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55165);