Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
970 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)(18,19,24,27,23,28,22,36)(20,29,38,40,31,46,32,25)(21,26,37,42,35,43,34,44)(30,45,48,39,47,41,33,49);(14,15)(16,17)(18,20,22,32,23,31,24,38)(19,25,27,29,28,40,36,46)(21,33,34,47,35,48,37,30)(26,41,42,49,43,45,44,39);(15,17)(18,21,23,35)(19,26,28,43)(20,30,31,47)(22,37,24,34)(25,39,40,49)(27,44,36,42)(29,45,46,41)(32,48,38,33);(20,31)(25,40)(29,46)(30,47)(32,38)(33,48)(39,49)(41,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16591);