Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
886 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)(14,15,20,25)(16,26,17,28)(18,23,19,24)(21,29,22,27)(30,31,35,33)(32,38,40,45)(34,42,44,37)(36,43,39,41);(14,16,20,17)(15,21,25,22)(18,29,19,27)(23,26,24,28)(30,32,35,40)(31,36,33,39)(34,43,44,41)(37,45,42,38);(14,17,20,16)(15,22,25,21)(18,29,19,27)(23,26,24,28)(30,33,35,31)(32,39,40,36)(34,37,44,42)(38,43,45,41);(14,18,20,19)(15,23,25,24)(16,27,17,29)(21,28,22,26)(32,40)(36,39)(38,45)(41,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12037);