Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C11⋊AGL(1,𝔽23)) |
| unambiguous semidirect product | C11⋊(C5⋊AGL(1,𝔽23)) |
| unambiguous semidirect product | (C23⋊C11)⋊D55 |
| unambiguous semidirect product | D1265⋊C11 |
| Fitting, socle, derived | C5×C11×C23 ⋊ C2×C11 |
| Hall | C5×C11×C23⋊C11 ⋊ C2 |
| Hall | C11×C23⋊C11 ⋊ D5 |
| Hall | C5×C23 ⋊ C11×D11 |
| Sylow | C23 ⋊ C11×D55 |
| Sylow | C5 ⋊ C11⋊AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C23 | C2×C11 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1265 |
Polycyclic presentation:
2,11,5,11,23|c^a=c^4,d^a=d^10,e^a=e^22,e^b=e^2374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 27);