Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32898 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32928 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C2×C13×B(4,𝔽2) | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1618 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,24)(21,25)(22,23)(26,32)(27,29)(28,30)(31,33);(14,15,16,17)(19,23)(24,29)(25,30)(31,32);(18,20)(19,24)(21,26)(22,27)(23,29)(25,31)(28,33)(30,32);(18,21)(19,25)(20,26)(22,28)(23,30)(24,31)(27,33)(29,32)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25916);