Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3559 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(17,24)(20,28)(21,25)(22,26)(27,29)(30,31,34,37)(32,38,39,45)(33,41,42,36)(35,43,44,40);(14,15)(16,20)(17,25)(18,21)(19,24)(22,27)(23,29)(26,28)(33,42)(36,41)(38,45)(40,43);(14,16,18,23)(15,20,21,29)(17,26,24,22)(19,27,25,28)(30,32)(31,35)(33,43)(34,39)(36,45)(37,44)(38,41)(40,42);(15,21)(19,25)(20,29)(27,28)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12011);