Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18400 |
| 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 | |
978 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)(15,22)(16,27)(17,29)(18,32)(23,38)(24,40)(25,33)(26,39)(28,31)(30,43)(34,35)(36,45)(37,41)(42,44);(14,15)(16,23)(17,30)(18,33)(19,36)(20,25)(21,26)(22,32)(24,27)(28,43)(29,41)(31,38)(34,39)(35,45)(37,42)(40,44);(14,16,21,17)(15,23,26,30)(18,31,35,28)(19,27,20,29)(22,37,39,40)(24,25,41,36)(32,42,34,44)(33,38,45,43);(14,17,21,16)(15,24,26,41)(18,31,35,28)(19,29,20,27)(22,38,39,43)(23,25,30,36)(32,42,34,44)(33,37,45,40)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11388);