Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62013 |
| 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 | |
1790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23)(24,29)(25,37)(26,31)(27,40)(28,32)(30,38)(33,47)(34,43)(35,44)(36,50)(39,45)(41,46)(42,48)(49,52)(51,53);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,33)(26,34)(27,36)(28,35)(30,42)(31,43)(32,44)(37,47)(38,48)(39,49)(40,50)(41,51)(45,52)(46,53);(22,25,28,39)(23,30,32,46)(24,33,35,49)(26,38,27,41)(29,42,44,53)(31,45,40,37)(34,48,36,51)(43,52,50,47);(15,18)(19,21)(22,26,28,27)(23,31,32,40)(24,34,35,36)(25,38,39,41)(29,43,44,50)(30,45,46,37)(33,48,49,51)(42,52,53,47);(14,16,17,20)(15,19,18,21)(24,35)(29,44)(33,49)(34,36)(42,53)(43,50)(47,52)(48,51)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55001);