Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
980 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)(18,19,24,28,25,30,23,29)(20,31,33,26,21,35,34,42)(22,37,38,27,40,44,39,45)(32,41,48,49,36,43,47,46);(14,15)(16,17)(18,20,24,33,25,21,23,34)(19,26,28,35,30,42,29,31)(22,36,38,47,40,32,39,48)(27,43,44,46,45,41,37,49);(15,17)(18,21,25,20)(19,26,30,42)(22,36,40,32)(23,34,24,33)(27,41,45,43)(28,31,29,35)(37,49,44,46)(38,48,39,47);(18,22)(19,27)(20,32)(21,36)(23,39)(24,38)(25,40)(26,41)(28,44)(29,37)(30,45)(31,46)(33,48)(34,47)(35,49)(42,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18182);