Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#25050 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3060 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(16,18)(17,19)(20,21)(22,23)(24,34)(25,38)(26,42)(27,33)(28,32)(29,36)(30,37)(31,39)(35,49)(40,52)(41,47)(43,45)(44,51)(46,53)(48,50);(14,16,17,20)(15,18,19,21)(22,24,28,43,27,37,26,36)(23,29,42,30,33,45,32,34)(25,35,41,53,40,51,39,50)(31,44,52,46,47,49,38,48);(15,19)(18,21)(22,24)(23,30)(25,35)(26,36)(27,37)(28,43)(29,32)(31,46)(33,34)(38,44)(39,50)(40,51)(41,53)(42,45)(47,48)(49,52);(22,25,26,39,27,40,28,41)(23,31,32,38,33,47,42,52)(24,35,36,50,37,51,43,53)(29,44,34,48,45,49,30,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18038);