Finite Group DatabasebetaFinite Group Databasebeta| order | 10810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×AGL(1,𝔽47) |
| unambiguous semidirect product | D47⋊(C5×C23) |
| unambiguous semidirect product | (C5×D47)⋊C23 |
| unambiguous semidirect product | (C47⋊C23)⋊(C2×C5) |
| Fitting, socle, Hall | C5×C47 ⋊ C2×C23 |
| derived, Sylow | C47 ⋊ C2×C5×C23 |
| Hall | C5×C47⋊C23 ⋊ C2 |
| Hall | C47⋊C23 ⋊ C2×C5 |
| Hall | C5×D47 ⋊ C23 |
| Hall | D47 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | AGL(1,𝔽47) |
| commutator, cosocle, hypocenter | C47 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C47 | C2×C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10810, 10);