Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18306 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1040 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)(15,20)(16,24)(17,28)(21,33)(22,31)(23,29)(26,40)(27,38)(30,39)(32,35)(34,43)(36,45)(37,42)(41,44);(14,15)(16,21)(17,29)(18,23)(19,22)(20,28)(24,35)(25,34)(26,41)(27,36)(30,43)(31,39)(32,42)(33,40)(37,45)(38,44);(17,30)(20,31)(26,37)(28,39)(29,43)(32,33)(40,42)(41,45);(14,16,25,38)(15,21,34,44)(17,26,39,40)(18,27,19,24)(20,32,43,45)(22,35,23,36)(28,42,30,37)(29,41,31,33)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11294);