Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18435 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
922 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)(25,37)(27,41)(30,40)(32,36)(34,44)(35,43)(38,39)(42,45);(14,15,18,23)(16,21,25,34)(17,29,28,20)(19,22,26,35)(24,36,37,45)(27,42,39,32)(30,43,40,31)(33,38,44,41);(16,25)(17,30)(20,31)(21,34)(24,37)(27,41)(28,40)(29,43)(32,44)(33,42)(36,45)(38,39);(14,16,26,37)(15,21,35,45)(17,27,40,41)(18,25,19,24)(20,32,43,44)(22,36,23,34)(28,39,30,38)(29,42,31,33)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11423);