Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61635 |
| 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 | |
2070 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)(25,36)(26,31)(27,40)(28,32)(30,37)(33,48)(34,43)(35,44)(38,46)(39,45)(41,47)(42,51)(49,52)(50,53);(14,16)(15,18)(17,21)(19,20)(22,24)(23,29)(25,33)(26,39)(27,34)(28,35)(30,42)(31,45)(32,44)(36,48)(37,51)(38,50)(40,43)(41,49)(46,53)(47,52);(22,25)(23,30)(24,33)(26,37)(27,41)(28,38)(29,42)(31,46)(32,47)(34,49)(35,50)(36,40)(39,51)(43,48)(44,52)(45,53);(16,21)(18,20)(22,26,28,27)(23,31,32,40)(24,34,35,39)(25,37,38,41)(29,43,44,45)(30,46,47,36)(33,49,50,51)(42,48,52,53);(15,19)(18,20)(24,35)(29,44)(33,50)(34,39)(42,52)(43,45)(48,53)(49,51)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54623);