Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#9027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
660 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,20,23,21,24,25,22)(26,27)(28,31)(29,36,37,32)(30,33)(34,38,40,41)(35,39);(14,15,16,17)(19,22)(20,25)(23,24)(26,28,30,35)(27,31,33,39)(29,34,37,40)(32,38,36,41);(26,29,30,37)(27,32,33,36)(28,34,35,40)(31,38,39,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2015);