Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32696 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
552 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)(14,15,18,23,19,22,33,39)(16,24,27,40,26,20,32,35)(17,28,31,44,30,21,36,38)(25,41,29,43,42,34,45,37);(14,16)(15,20)(17,29)(18,32)(19,26)(21,37)(22,24)(23,40)(25,31)(27,33)(28,43)(30,45)(34,38)(35,39)(36,42)(41,44);(14,17)(15,21,22,28)(16,25,26,42)(18,31)(19,30)(20,34)(23,38,39,44)(24,41)(27,29,32,45)(33,36)(35,37)(40,43);(15,22)(18,33)(21,28)(27,32)(29,45)(31,36)(35,40)(37,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25684);