Finite Group DatabasebetaFinite Group Databasebeta| order | 33660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C3×C17×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C17 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C3×C17 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C3×C17 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 561 |
A minimal faithful permutation representation — 2 generators on 31 points:
(4,6,14,10,8)(5,13,9,12,11);(1,2,3)(4,6,9)(5,7,11)(10,12,13)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33660, 386);