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×#33653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
568 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)(16,19)(17,18)(20,21)(22,23,28,33)(24,29,36,47)(25,31,27,43)(26,39,42,53)(30,48,50,35)(32,38,51,41)(34,44,37,46)(40,45,52,49);(15,18)(19,21)(22,24)(23,29)(25,37)(26,35)(27,34)(28,36)(30,39)(31,46)(32,45)(33,47)(38,52)(40,41)(42,48)(43,44)(49,51)(50,53);(14,16,17,20)(15,19,18,21)(22,24)(23,30)(25,34)(26,40)(27,37)(28,36)(29,39)(31,45)(32,46)(33,50)(35,41)(38,48)(42,52)(43,49)(44,51)(47,53);(22,25,28,27)(23,31,33,43)(24,34,36,37)(26,38,42,41)(29,44,47,46)(30,45,50,49)(32,39,51,53)(35,40,48,52)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26641);