Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33844 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
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)(18,19,24,28)(20,29,30,48)(21,34,26,46)(22,37,40,36)(23,41,39,27)(25,43,44,32)(31,49,45,38)(33,35,42,47);(18,20,24,30)(19,25,28,44)(21,35,26,47)(22,38,40,49)(23,42,39,33)(27,31,41,45)(29,36,48,37)(32,46,43,34);(15,17)(20,30)(25,44)(29,48)(31,45)(32,43)(33,42)(35,47)(38,49);(18,21,24,26)(19,22,28,40)(20,31,30,45)(23,37,39,36)(25,33,44,42)(27,46,41,34)(29,43,48,32)(35,49,47,38)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26832);