Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61550 |
| 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) = 832 |
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)(22,23,27,30)(24,28,33,43)(25,35,38,47)(26,39,41,31)(29,40,46,37)(32,48,36,53)(34,51,50,44)(42,52,45,49);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,36)(26,34)(27,33)(29,45)(30,43)(31,44)(32,38)(35,53)(37,52)(39,51)(40,49)(41,50)(42,46)(47,48);(22,25,27,38)(23,29,30,46)(24,32,33,36)(26,40,41,37)(28,42,43,45)(31,47,39,35)(34,52,50,49)(44,53,51,48);(15,18)(19,21)(23,30)(28,43)(29,46)(31,39)(35,47)(42,45)(44,51)(48,53);(14,16,17,20)(15,19,18,21)(23,30)(24,33)(29,46)(31,39)(32,36)(34,50)(35,47)(49,52)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54538);