Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24805 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24807 |
| 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 | |
844 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)(20,32,41,28,22,40,34,26)(21,35,37,27,39,45,38,44)(33,43,47,46,36,42,48,49);(14,15)(16,17)(18,20,23,34,24,22,25,41)(19,26,29,32,31,28,30,40)(21,33,37,47,39,36,38,48)(27,42,35,46,44,43,45,49);(15,17)(18,21)(19,27)(20,33)(22,36)(23,37)(24,39)(25,38)(26,42)(28,43)(29,35)(30,45)(31,44)(32,46)(34,47)(40,49)(41,48);(18,22,25,34,24,20,23,41)(19,28,30,32,31,26,29,40)(21,36,38,47,39,33,37,48)(27,43,45,46,44,42,35,49)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17795);