Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C23⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C11⋊C5)⋊(C11×D23) |
| Fitting, socle, Hall | C112×C23 ⋊ C2×C5 |
| derived | C11×C23 ⋊ C2×C5×C11 |
| Hall | C11×C23×C11⋊C5 ⋊ C2 |
| Hall | C11×D253 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ D23 |
| Sylow | C112 ⋊ C5×D23 |
| Sylow | C23 ⋊ C11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C23⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11×C23 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | C2×C5 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C11 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2530 |
968 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 34);