Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33594 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×#459 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
696 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)(17,30)(18,24)(19,34)(20,35)(21,26)(22,28)(23,27)(29,42)(31,45)(32,41)(33,37)(36,38)(39,43)(40,44);(14,16,19,28,21,29,18,20)(15,22,24,25,26,35,34,42)(17,27,32,43,33,44,31,36)(23,37,38,41,40,30,39,45);(14,17)(15,23)(16,27)(18,31)(19,32)(20,36)(21,33)(22,37)(24,38)(25,41)(26,40)(28,43)(29,44)(30,35)(34,39)(42,45);(14,18,21,19)(15,24,26,34)(16,20,29,28)(17,31,33,32)(22,25,35,42)(23,38,40,39)(27,36,44,43)(30,45,37,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26582);