Finite Group DatabasebetaFinite Group Databasebeta| order | 22660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C11×C103 ⋊ C22×C5 |
| Hall | C11⋊C5×C103 ⋊ C22 |
| Hall | D11×D103 ⋊ C5 |
| Sylow | C103 ⋊ C2×AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ C2×D103 |
| Sylow | C11 ⋊ C2×C5×D103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C103 | C22×C5 |
| LCS | G ▷ C11×C103 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1133 |
583 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22660, 14);