Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61676 |
| 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×#532 ◁ G | |
2024 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)(24,31)(25,38)(26,34)(27,33)(28,32)(29,37)(30,40)(35,50)(36,45)(39,53)(41,49)(42,48)(43,47)(44,51)(46,52);(14,16)(15,18)(17,21)(19,20)(22,24,27,37)(23,29,33,31)(25,39,41,35)(26,42,28,36)(30,46,47,44)(32,48,34,45)(38,50,49,53)(40,51,43,52);(22,25,27,41)(23,30,33,47)(24,35,37,39)(26,40,28,43)(29,44,31,46)(32,38,34,49)(36,51,42,52)(45,50,48,53);(16,21)(18,20)(22,24)(23,31)(25,35)(26,42)(27,37)(28,36)(29,33)(30,46)(32,45)(34,48)(38,50)(39,41)(40,52)(43,51)(44,47)(49,53);(15,19)(18,20)(22,26,27,28)(23,32,33,34)(24,36,37,42)(25,40,41,43)(29,45,31,48)(30,38,47,49)(35,51,39,52)(44,50,46,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54664);