Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C2×C42 |
| direct product | C13×#17303 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(24,26)(25,28)(27,29)(30,31,33,35)(32,36,37,34)(40,44)(42,45);(15,18)(16,20)(23,24)(27,28)(32,37)(34,36)(38,39,41,43)(40,45,44,42);(14,15,17,18)(16,19,20,21)(22,24,26,23)(25,27,29,28)(30,31)(32,34)(33,35)(36,37)(38,40,41,44)(39,42,43,45);(14,16)(15,19)(17,20)(18,21)(22,25,26,29)(23,27,24,28)(30,32)(31,34)(33,37)(35,36)(38,39)(40,42)(41,43)(44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10291);