Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32944 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1294 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)(18,19,24,29)(20,30,32,41)(21,35,37,43)(22,28,23,27)(25,34,40,33)(26,38,42,36)(31,45,46,39)(44,48,49,47);(18,20,23,34,24,32,22,33)(19,25,28,41,29,40,27,30)(21,31,38,48,37,46,36,47)(26,39,43,49,42,45,35,44);(18,21)(19,26)(20,31)(22,36)(23,38)(24,37)(25,39)(27,35)(28,43)(29,42)(30,44)(32,46)(33,47)(34,48)(40,45)(41,49);(15,17)(20,32)(25,40)(30,41)(31,46)(33,34)(39,45)(44,49)(47,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25934);