Finite Group DatabasebetaFinite Group Databasebeta| order | 30866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C61⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊D61 |
| unambiguous semidirect product | D1403⋊C11 |
| Fitting, socle, derived, Hall | C23×C61 ⋊ C2×C11 |
| Hall | C61×C23⋊C11 ⋊ C2 |
| Hall | D1403 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D61 |
| Sylow | C61 ⋊ AGL(1,𝔽23) |
| Sylow | C23 ⋊ C11×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C61 | C2×C11 |
| LCS | G ▷ C23×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1403 |
Polycyclic presentation:
2,11,23,61|c^a=c^22,d^a=d^60,c^b=c^2413 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30866, 12);