Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#21946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G | |
1010 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)(14,15,16,17)(18,19)(20,24)(21,23)(22,25)(27,32)(28,35)(29,31)(33,40)(36,41)(37,38);(18,20)(19,22)(21,25)(23,24)(26,27)(28,36)(29,39)(30,32)(31,34)(33,38)(35,40)(37,41);(20,25)(22,24)(26,28,31,35,30,38,29,37)(27,33,34,41,32,36,39,40);(19,23)(22,24)(26,29,30,31)(27,34,32,39)(28,37,38,35)(33,41,36,40)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14934);