Finite Group DatabasebetaFinite Group Databasebeta| order | 10810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1081 |
| unambiguous semidirect product | C23⋊(C5×D47) |
| unambiguous semidirect product | C47⋊(C5×D23) |
| Fitting, socle, Hall | C5×C23×C47 ⋊ C2 |
| derived, Hall | C23×C47 ⋊ C2×C5 |
| Hall | C5×C47 ⋊ D23 |
| Hall | C5×C23 ⋊ D47 |
| Sylow | C47 ⋊ C5×D23 |
| Sylow | C23 ⋊ C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1081 |
| commutator, cosocle, hypocenter | C23×C47 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C47 | C2 |
| LCS | G ▷ C23×C47 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
2710 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D23×D47, D5×D1081, D115⋊D47, … |
| maximal normal subgroup of | C5×D23×D47, D5×D1081, D115⋊D47, … |
| maximal quotient of | C5×Dic1081, C2×C5×D1081, C3×C5×D1081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10810, 5);