Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#577 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1328 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)(20,25)(21,33)(22,24)(23,28)(26,34)(27,37)(29,40)(30,45)(31,38)(32,41)(35,42)(36,43)(39,44)(46,48)(47,49);(19,24)(20,29)(22,37)(26,33)(27,28)(30,44)(31,32)(34,35)(38,40)(42,43)(45,48)(46,47);(15,17)(18,20,23,32)(19,25,28,41)(21,30,36,46)(22,31,37,29)(24,38,27,40)(26,39,42,49)(33,45,43,48)(34,44,35,47);(18,21)(19,26)(20,30)(22,35)(23,36)(24,33)(25,39)(27,43)(28,42)(29,44)(31,47)(32,46)(34,37)(38,45)(40,48)(41,49)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17446);