Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
656 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)(17,29)(18,30)(22,37)(23,34)(27,28)(31,42)(32,36)(35,43)(38,40)(39,45);(14,15,18,20,19,23,30,34)(16,25,24,32,28,21,27,36)(17,22,29,33,31,37,42,44)(26,39,38,43,41,35,40,45);(14,16)(15,21)(17,26)(18,27)(19,28)(20,32)(22,35)(23,25)(24,30)(29,40)(31,41)(33,43)(34,36)(37,39)(38,42)(44,45);(14,17,30,42,19,31,18,29)(15,22,34,44,23,37,20,33)(16,26,24,38,28,41,27,40)(21,35,36,45,25,39,32,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17976);