Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#15483 |
| 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 | |
1386 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)(18,19)(20,22)(21,24)(23,25)(26,27,29,30)(28,32,33,31)(34,35)(36,41)(37,39)(38,40);(19,20)(21,25)(27,30)(31,32)(34,36,38,37)(35,39,40,41);(18,20,22,19)(21,24,25,23)(26,28,29,33)(27,31,30,32)(34,37,38,36)(35,39,40,41);(14,15)(16,17)(18,21)(19,23)(20,24)(22,25)(26,27)(28,31)(29,30)(32,33)(34,35)(36,41)(37,39)(38,40)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8471);