Finite Group DatabasebetaFinite Group Databasebeta| order | 37620 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C2 |
| direct product | C3×C19×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C19 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C3×C19 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C3×C19 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 627 |
A minimal faithful permutation representation — 2 generators on 33 points:
(4,12,14,13,11,5,7,10,6,9,8);(1,2,3)(4,10)(7,13)(8,9)(12,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33)456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37620, 505);