Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3283 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
548 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)(16,20,21,18)(22,23,28,33)(24,34,35,51)(25,32,27,30)(26,39,42,47)(29,44,45,37)(31,38,49,41)(36,52,43,48)(40,50,53,46);(14,16)(15,18)(17,21)(19,20)(24,35)(29,45)(34,51)(36,43)(37,44)(40,53)(46,50)(48,52);(22,24)(23,29)(25,36)(26,40)(27,43)(28,35)(30,46)(31,48)(32,50)(33,45)(34,39)(37,41)(38,44)(42,53)(47,51)(49,52);(16,21)(18,20)(22,25,28,27)(23,30,33,32)(24,36,35,43)(26,38,42,41)(29,46,45,50)(31,47,49,39)(34,48,51,52)(37,40,44,53)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26886);