Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19043 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3558 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
950 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)(30,31,34,37)(32,38,39,45)(33,41,43,36)(35,42,44,40);(14,16)(15,20)(17,27)(18,25)(19,26)(21,24)(22,28)(23,29)(30,32)(31,35)(33,42)(34,39)(36,45)(37,44)(38,41)(40,43);(14,16)(15,20)(17,25)(18,27)(19,26)(21,28)(22,24)(23,29)(33,43)(36,41)(38,45)(40,42);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,29,24)(32,39)(35,44)(38,45)(40,42)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12031);