Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24802 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,25,29,24,31,23,30)(20,28,22,40,34,42,33,26)(21,35,37,27,39,45,38,44)(32,46,47,43,48,41,36,49);(14,15)(16,17)(18,20,23,33,24,34,25,22)(19,26,29,28,31,40,30,42)(21,32,37,47,39,48,38,36)(27,41,35,43,44,46,45,49);(15,17)(18,21)(19,27)(20,32)(22,36)(23,37)(24,39)(25,38)(26,41)(28,43)(29,35)(30,45)(31,44)(33,47)(34,48)(40,46)(42,49);(18,22,25,34,24,33,23,20)(19,28,30,26,31,42,29,40)(21,36,38,48,39,47,37,32)(27,43,45,41,44,49,35,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17792);