Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61627 |
| 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×#525 ◁ G | |
2050 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)(14,15)(16,20)(17,19)(18,21)(22,23)(24,29)(25,37)(26,31)(27,40)(28,32)(30,38)(33,48)(34,43)(35,44)(36,45)(39,46)(41,47)(42,49)(50,53)(51,52);(14,16)(15,18)(17,21)(19,20)(22,24)(23,29)(25,33)(26,34)(27,35)(28,36)(30,42)(31,43)(32,45)(37,48)(38,49)(39,51)(40,44)(41,50)(46,52)(47,53);(22,25,28,39)(23,30,32,47)(24,33,36,51)(26,38,27,41)(29,42,45,53)(31,46,40,37)(34,49,35,50)(43,52,44,48);(16,21)(18,20)(22,26,28,27)(23,31,32,40)(24,34,36,35)(25,38,39,41)(29,43,45,44)(30,46,47,37)(33,49,51,50)(42,52,53,48);(15,19)(18,20)(22,26,28,27)(23,31,32,40)(24,35,36,34)(25,38,39,41)(29,44,45,43)(30,46,47,37)(33,50,51,49)(42,48,53,52)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54615);