Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#17593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C42×C13 ◁ G | |
1042 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)(15,21,23,35)(16,26)(17,31)(18,32)(22,37,38,45)(24,36,25,33)(28,42)(29,43)(30,41)(34,39,44,40);(14,15)(16,22)(17,21)(18,33)(19,24)(20,25)(23,27)(26,40)(28,34)(29,37)(30,39)(31,36)(32,35)(38,41)(42,44)(43,45);(14,16,27,41)(15,22,23,38)(17,28,32,42)(18,29,31,43)(19,30,20,26)(21,34,35,44)(24,39,25,40)(33,37,36,45);(14,17,20,18)(15,21,25,33)(16,28,26,29)(19,31,27,32)(22,34,40,37)(23,35,24,36)(30,43,41,42)(38,44,39,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10581);