Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18345 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,24,26,28)(17,21,18,22)(20,27,29,25)(31,35)(33,40)(36,44)(37,41)(38,42)(43,45);(14,16)(15,20)(17,25)(18,27)(19,26)(21,28)(22,24)(23,29)(30,31)(32,36)(33,41)(34,37)(35,40)(38,43)(39,45)(42,44);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,29,24)(30,32,34,39)(31,36,37,45)(33,42,40,38)(35,43,41,44);(14,17,19,18)(15,22,23,21)(16,25,26,27)(20,24,29,28)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11333);