Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26080 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,20,21,18)(22,23,27,33)(24,34,37,30)(25,38,40,52)(26,42,28,32)(29,43,45,36)(31,41,47,39)(35,49,51,44)(46,50,48,53);(22,24,26,36,27,37,28,43)(23,29,32,34,33,45,42,30)(25,35,39,50,40,51,41,53)(31,44,38,48,47,49,52,46);(14,16,17,21)(15,18,19,20)(22,24,27,37)(23,30,33,34)(25,35,40,51)(26,36,28,43)(29,42,45,32)(31,46,47,48)(38,44,52,49)(39,50,41,53);(22,25,26,39,27,40,28,41)(23,31,32,38,33,47,42,52)(24,35,36,50,37,51,43,53)(29,44,34,48,45,49,30,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19068);