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×#24461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1318 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)(20,29)(21,35)(22,38)(23,27)(24,28)(25,32)(26,36)(30,34)(31,40)(33,41)(37,42)(39,43)(44,46)(45,48)(47,49);(18,20,24,34)(19,25,28,41)(21,31,37,47)(22,33,23,32)(26,40,43,49)(27,30,38,29)(35,44,42,45)(36,48,39,46);(15,17)(18,19)(20,30)(21,26)(22,27)(23,38)(24,28)(25,32)(29,34)(31,45)(33,41)(35,36)(37,43)(39,42)(40,48)(44,47)(46,49);(18,21,24,37)(19,26,28,43)(20,31,34,47)(22,39,23,36)(25,40,41,49)(27,42,38,35)(29,44,30,45)(32,48,33,46)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17449);