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×#25197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
968 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)(14,15,19,23,20,24,18,32)(16,25,27,21,28,36,33,37)(17,29,30,39,31,38,34,22)(26,41,43,45,44,35,42,40);(14,16,19,27,20,28,18,33)(15,21,23,36,24,37,32,25)(17,26,30,43,31,44,34,42)(22,35,29,40,39,41,38,45);(14,17)(15,22)(16,26)(18,30)(19,34)(20,31)(21,35)(23,38)(24,39)(25,40)(27,42)(28,44)(29,32)(33,43)(36,45)(37,41);(14,15,20,24)(16,21,28,37)(17,22,31,39)(18,32,19,23)(25,27,36,33)(26,35,44,41)(29,34,38,30)(40,42,45,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18185);