Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60660 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C22×C13 | C23×D4 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
1770 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)(14,15,17,19)(16,20,21,18)(22,23)(24,29)(25,37)(26,31)(27,41)(28,32)(30,39)(33,46)(34,43)(35,44)(36,50)(38,45)(40,51)(42,49)(47,53)(48,52);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,33)(26,35)(27,36)(28,34)(30,42)(31,44)(32,43)(37,46)(38,48)(39,49)(40,47)(41,50)(45,52)(51,53);(22,25,27,39,28,40,26,38)(23,30,31,37,32,45,41,51)(24,33,36,49,34,47,35,48)(29,42,44,46,43,52,50,53);(24,34)(29,43)(33,47)(35,36)(42,52)(44,50)(46,53)(48,49);(22,26,28,27)(23,31,32,41)(24,35,34,36)(25,38,40,39)(29,44,43,50)(30,37,45,51)(33,48,47,49)(42,46,52,53)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53648);