Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33630 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
542 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)(22,23,26,29)(24,34,36,51)(25,33,28,31)(27,40,39,48)(30,46,44,37)(32,38,45,42)(35,52,43,49)(41,50,53,47);(14,16,17,21)(15,18,19,20)(23,29)(30,44)(31,33)(32,45)(34,51)(40,48)(47,50)(49,52);(22,24)(23,30)(25,35)(26,36)(27,41)(28,43)(29,44)(31,47)(32,49)(33,50)(34,40)(37,42)(38,46)(39,53)(45,52)(48,51);(22,25,26,28)(23,31,29,33)(24,35,36,43)(27,38,39,42)(30,47,44,50)(32,48,45,40)(34,49,51,52)(37,41,46,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26618);