Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61487 |
| 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 | |
1800 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)(19,21)(22,23,27,32)(24,33,36,29)(25,37,39,46)(26,31,28,41)(30,42,47,38)(34,49,51,53)(35,45,40,44)(43,52,48,50);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,34)(26,40)(27,36)(28,35)(30,43)(31,45)(32,33)(37,53)(38,52)(39,51)(41,44)(42,50)(46,49)(47,48);(22,25)(23,30)(24,34)(26,38)(27,39)(28,42)(29,43)(31,46)(32,47)(33,48)(35,50)(36,51)(37,41)(40,52)(44,53)(45,49);(15,18)(19,21)(22,26,27,28)(23,31,32,41)(24,35,36,40)(25,38,39,42)(29,44,33,45)(30,46,47,37)(34,50,51,52)(43,53,48,49);(14,16,17,20)(15,19,18,21)(24,36)(29,33)(34,51)(35,40)(43,48)(44,45)(49,53)(50,52)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54475);