Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61502 |
| 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 | |
1788 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
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)(24,33)(25,37)(26,31)(27,32)(28,42)(29,36)(30,39)(34,50)(35,46)(38,53)(40,48)(41,45)(43,49)(44,51)(47,52);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,38)(26,41)(27,36)(28,35)(30,47)(31,46)(32,33)(34,40)(37,50)(39,51)(42,45)(43,52)(44,49)(48,53);(22,25,27,40)(23,30,32,49)(24,34,36,38)(26,39,28,43)(29,44,33,47)(31,48,42,37)(35,51,41,52)(45,53,46,50);(15,18)(19,21)(22,26,27,28)(23,31,32,42)(24,35,36,41)(25,39,40,43)(29,45,33,46)(30,48,49,37)(34,51,38,52)(44,53,47,50);(14,16,17,20)(15,19,18,21)(24,36)(29,33)(34,38)(35,41)(44,47)(45,46)(50,53)(51,52)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54490);