Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊(C5×D11) |
| unambiguous semidirect product | (C5×D253)⋊C11 |
| Fitting, socle | C5×C11×C23 ⋊ C2×C11 |
| derived | C11×C23 ⋊ C2×C5×C11 |
| Hall | C5×C11×C23⋊C11 ⋊ C2 |
| Hall | C11×C23⋊C11 ⋊ C2×C5 |
| Hall | C5×C23 ⋊ C11×D11 |
| Sylow | C23 ⋊ C5×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C11×C23 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C23 | C2×C11 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1265 |
440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 23);