Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25×C4 |
| direct product | C13×#15188 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,20)(23,24)(28,33)(29,31);(15,17)(19,20)(22,23,25,24)(26,27,30,32)(28,31,33,29);(14,15)(16,17)(18,20,21,19)(22,24,25,23)(26,28)(27,31)(29,32)(30,33);(26,29,30,31)(27,28,32,33)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8176);