Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#32845 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C13×#376 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,18,20,21)(22,23)(24,28)(25,29)(26,27)(30,36)(31,34)(32,35)(33,37)(38,39,41,43)(40,46,48,44)(42,45,49,51)(47,52,50,53);(14,16)(15,18)(17,20)(19,21)(23,27)(25,32)(28,34)(30,33)(39,43)(40,47)(42,49)(44,52)(46,53)(48,50);(15,19)(18,21)(22,24,26,31)(23,28,27,34)(25,33,32,30)(29,37,35,36)(38,40,41,48)(39,44,43,46)(42,50,49,47)(45,52,51,53);(16,20)(18,21)(22,25,26,32)(23,29,27,35)(24,30,31,33)(28,36,34,37)(39,43)(40,48)(45,51)(47,50)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25833);