Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
990 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)(14,15,20,24,21,25,19,35)(16,26,28,22,29,39,36,40)(17,30,32,41,18,33,34,23)(27,38,44,45,31,37,43,42);(14,16,20,28,21,29,19,36)(15,22,24,39,25,40,35,26)(17,31,32,43,18,27,34,44)(23,38,30,45,41,37,33,42);(14,17,21,18)(15,23,25,41)(16,27,29,31)(19,32,20,34)(22,37,40,38)(24,33,35,30)(26,42,39,45)(28,43,36,44);(14,18,21,17)(15,23,25,41)(16,27,29,31)(19,32,20,34)(22,38,40,37)(24,30,35,33)(26,42,39,45)(28,44,36,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18187);