Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33633 |
| 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 ◁ C13×#117 ◁ C13×#405 ◁ G | |
534 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)(24,29)(25,31)(26,39)(27,43)(28,33)(30,35)(32,41)(34,44)(36,47)(37,46)(38,50)(40,45)(42,53)(48,52)(49,51);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,37)(26,35)(27,34)(28,36)(30,39)(31,46)(32,45)(33,47)(38,52)(40,41)(42,51)(43,44)(48,50)(49,53);(22,24)(23,30)(25,34)(26,40)(27,37)(28,36)(29,39)(31,45)(32,46)(33,49)(35,41)(38,51)(42,52)(43,48)(44,50)(47,53);(22,25,28,27)(23,31,33,43)(24,34,36,37)(26,38,42,41)(29,44,47,46)(30,45,49,48)(32,39,50,53)(35,40,51,52)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26621);