Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3012 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1010 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)(18,19,23,30,25,31,24,29)(20,32,36,46,37,45,35,26)(21,38,41,28,22,42,40,27)(33,43,34,44,49,48,39,47);(14,15)(16,17)(18,20,23,36,25,37,24,35)(19,26,30,32,31,46,29,45)(21,39,41,33,22,34,40,49)(27,47,38,43,28,44,42,48);(15,17)(18,21,25,22)(19,27,31,28)(20,33,37,49)(23,40,24,41)(26,43,46,48)(29,38,30,42)(32,47,45,44)(34,36,39,35);(18,22,25,21)(19,28,31,27)(20,34,37,39)(23,40,24,41)(26,44,46,47)(29,38,30,42)(32,48,45,43)(33,36,49,35)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18179);