Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#17304 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23,25,27)(24,28,29,26)(30,31)(32,35)(33,34)(36,37)(39,41)(40,44);(15,18)(16,20)(24,29)(26,28)(31,33)(32,36)(38,39,42,41)(40,43,44,45);(14,15,17,18)(16,19,20,21)(22,23)(24,26)(25,27)(28,29)(30,32,34,36)(31,35,33,37)(38,40)(39,43)(41,45)(42,44);(14,16)(15,19)(17,20)(18,21)(22,24)(23,26)(25,29)(27,28)(30,33,34,31)(32,35,36,37)(38,41,42,39)(40,43,44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10292);