Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
862 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)(14,15,18,20)(16,22,24,29)(17,25,27,21)(19,26,28,23)(30,31,35,32)(33,40,41,45)(34,39,44,37)(36,43,38,42);(14,16)(15,19)(17,26)(18,24)(20,28)(21,29)(22,25)(23,27)(30,32,35,31)(33,38,41,36)(34,37,44,39)(40,43,45,42);(17,27)(21,25)(22,29)(23,26)(30,33)(31,36)(32,38)(34,43)(35,41)(37,45)(39,40)(42,44);(15,20)(19,28)(21,25)(22,29)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11995);