Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#15249 |
| 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 | |
1066 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)(22,23,25,27)(24,28,29,26)(30,31,34,35)(32,37,36,33)(40,44)(42,45);(15,18)(19,21)(31,35)(32,36)(38,39,41,43)(40,42,44,45);(14,15)(16,19)(17,18)(20,21)(22,23)(24,26)(25,27)(28,29)(30,32,34,36)(31,33,35,37)(38,39)(40,42)(41,43)(44,45);(14,16,17,20)(15,19,18,21)(22,24,25,29)(23,26,27,28)(30,33)(31,36)(32,35)(34,37)(38,40)(39,42)(41,44)(43,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8237);