Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9265 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#447 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,23,17,20)(16,24,26,21,27,28,25,29)(31,35,37,40)(32,38,39,41);(15,20,23,22)(21,24,29,28)(30,31,33,40,34,37,42,35)(32,36,41,44,39,45,38,43);(14,16)(15,21)(17,25)(18,26)(19,27)(20,24)(22,28)(23,29)(30,32)(31,36)(33,41)(34,39)(35,43)(37,45)(38,42)(40,44)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2253);