Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
950 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)(14,15,18,21)(16,20,17,19)(22,23,26,31)(24,33,35,29)(25,37,39,49)(27,41,28,32)(30,43,48,40)(34,51,52,47)(36,45,42,46)(38,44,53,50);(14,16,18,17)(15,19,21,20)(22,24,26,35)(23,29,31,33)(25,38,39,53)(27,36,28,42)(30,47,48,51)(32,45,41,46)(34,43,52,40)(37,50,49,44);(14,16,18,17)(15,20,21,19)(22,25,28,43,26,39,27,40)(23,30,41,49,31,48,32,37)(24,34,42,38,35,52,36,53)(29,44,46,51,33,50,45,47);(14,17,18,16)(15,20,21,19)(23,31)(25,39)(29,33)(32,41)(34,52)(38,53)(40,43)(45,46)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18915);