Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2635 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
996 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)(21,34)(22,32)(23,29)(25,40)(26,42)(27,39)(30,44)(33,35)(36,45)(37,41)(38,43);(14,15,18,23)(16,25,27,21)(17,29,28,20)(19,22,31,36)(24,37,39,35)(26,33,43,41)(30,45,44,32)(34,42,40,38);(17,30)(20,32)(26,38)(28,44)(29,45)(33,34)(40,41)(42,43);(14,16,18,27)(15,21,23,25)(17,26,28,43)(19,24,31,39)(20,33,29,41)(22,35,36,37)(30,38,44,42)(32,34,45,40)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11340);