Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#21783 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25,28,20)(17,29,31,22)(18,24)(19,23)(21,27,37,32)(26,34)(30,43,45,38)(33,35)(36,40)(39,41)(42,44);(14,16)(15,20)(17,26)(18,32)(19,28)(21,35)(22,34)(23,25)(24,37)(27,33)(29,39)(30,44)(31,41)(36,43)(38,42)(40,45);(14,16)(15,21)(17,26)(18,32)(19,28)(20,24)(22,36)(23,37)(25,35)(27,33)(29,42)(30,44)(31,41)(34,38)(39,43)(40,45);(14,17,19,31)(15,22,23,29)(16,26,28,41)(18,30,33,45)(20,34,25,39)(21,36,37,42)(24,38,35,43)(27,40,32,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14771);