Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62072 |
| 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 | |
1780 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)(22,23,27,32)(24,33,36,29)(25,38,40,45)(26,31,28,41)(30,42,46,39)(34,49,51,53)(35,48,37,44)(43,50,47,52);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,34)(26,35)(27,36)(28,37)(30,43)(31,44)(32,33)(38,53)(39,50)(40,51)(41,48)(42,52)(45,49)(46,47);(22,25,27,40)(23,30,32,46)(24,34,36,51)(26,39,28,42)(29,43,33,47)(31,45,41,38)(35,50,37,52)(44,49,48,53);(15,18)(19,21)(22,26,27,28)(23,31,32,41)(24,35,36,37)(25,39,40,42)(29,44,33,48)(30,45,46,38)(34,50,51,52)(43,49,47,53);(14,16,17,20)(15,19,18,21)(23,32)(24,36)(30,46)(31,41)(34,51)(35,37)(38,45)(50,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55060);