Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#15100 |
| 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 | |
1378 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(20,24)(23,25)(27,30)(28,32)(35,37)(36,40);(14,15)(16,17)(19,22)(23,25)(27,30)(31,33)(34,35,38,37)(36,39,40,41);(18,19,21,22)(20,23,24,25)(26,27,29,30)(28,31,32,33)(34,36)(35,39)(37,41)(38,40);(18,20)(19,23)(21,24)(22,25)(26,28,29,32)(27,31,30,33)(34,37,38,35)(36,41,40,39)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8088);