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×#24798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
846 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)(14,15,16,17)(18,19,23,29)(20,25,33,41)(21,34,37,43)(22,28,35,27)(24,32,39,31)(26,42,44,36)(30,45,48,38)(40,47,49,46);(18,20,22,31,23,33,35,32)(19,24,27,25,29,39,28,41)(21,30,36,46,37,48,42,47)(26,38,34,40,44,45,43,49);(15,17)(18,20)(19,25)(21,30)(22,31)(23,33)(24,28)(26,40)(27,39)(29,41)(32,35)(34,45)(36,46)(37,48)(38,43)(42,47)(44,49);(18,21,35,42,23,37,22,36)(19,26,28,43,29,44,27,34)(20,30,32,47,33,48,31,46)(24,38,41,49,39,45,25,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17786);