Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62036 |
| 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 | |
1766 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)(16,20)(22,23,28,33)(24,29,36,44)(25,38,40,47)(26,32,27,31)(30,41,46,39)(34,48,50,53)(35,45,37,43)(42,51,52,49);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,34)(26,35)(27,37)(28,36)(30,42)(31,43)(32,45)(33,44)(38,48)(39,49)(40,50)(41,51)(46,52)(47,53);(22,25,28,40)(23,30,33,46)(24,34,36,50)(26,39,27,41)(29,42,44,52)(31,38,32,47)(35,49,37,51)(43,48,45,53);(15,18)(19,21)(22,26,28,27)(23,31,33,32)(24,35,36,37)(25,39,40,41)(29,43,44,45)(30,38,46,47)(34,49,50,51)(42,48,52,53);(14,16,17,20)(15,19,18,21)(24,36)(29,44)(34,50)(35,37)(42,52)(43,45)(48,53)(49,51)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55024);