Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12849 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,27,22,25,30,32,23,24,29,31,20,26,28,33);(19,24)(21,29)(25,26)(28,30);(15,17)(19,25,24,26)(21,29)(27,33,31,32)(28,30)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5837);