Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17597 |
| 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×#3519 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×D4×C13 ◁ G | |
1060 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)(15,20,22,33)(16,25)(17,28)(21,35,37,44)(23,34,24,29)(26,39)(27,42)(30,43)(32,36,45,38)(40,41);(14,15)(16,21)(17,29)(18,23)(19,24)(20,30)(22,31)(25,38)(26,36)(27,35)(28,33)(32,40)(34,43)(37,39)(41,45)(42,44);(14,16)(15,21)(17,27)(18,26)(19,25)(20,32)(22,37)(23,36)(24,38)(28,41)(29,35)(30,40)(31,39)(33,45)(34,44)(42,43);(16,26)(21,36)(25,39)(27,41)(32,44)(35,45)(37,38)(40,42)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10585);