Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#7721 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C24×C13 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20,21,18)(17,19)(22,23)(24,31,33,36)(25,34)(26,29)(27,30)(28,32,37,35)(38,39,41,44,42,45,48,51)(40,43,47,50,46,49,52,53);(14,16)(15,18)(17,21)(19,20)(22,24,27,33)(23,28,30,37)(25,32,26,35)(29,36,34,31)(38,40)(39,43)(41,47)(42,46)(44,50)(45,49)(48,52)(51,53);(15,19)(18,20)(22,25,27,26)(23,29,30,34)(24,32,33,35)(28,36,37,31)(40,46)(43,49)(47,52)(50,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 709);