Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#3485 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
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)(20,28,31,24)(21,30)(22,29,33,26)(23,27)(25,32);(14,15)(16,17)(18,20,23,31)(19,24,27,28)(21,29,32,26)(22,30,33,25);(15,17)(18,21)(19,25)(20,29)(22,24)(23,32)(26,31)(27,30)(28,33);(18,22)(19,26)(20,30)(21,24)(23,33)(25,31)(27,29)(28,32)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17395);