Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#15051 |
| 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 | |
1022 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)(19,21)(22,23,25,27)(24,26,28,29)(30,31)(32,36)(33,37)(34,35)(39,40)(41,45);(15,18)(19,21)(31,35)(32,37)(38,39,42,40)(41,43,45,44);(14,15)(16,19)(17,18)(20,21)(22,23)(24,26)(25,27)(28,29)(30,32,34,37)(31,36,35,33)(38,40,42,39)(41,44,45,43);(14,16,17,20)(15,19,18,21)(22,24,25,28)(23,26,27,29)(30,33,34,36)(31,37,35,32)(38,41)(39,43)(40,44)(42,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8039);