Finite Group DatabasebetaFinite Group Databasebeta| order | 5060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic253 |
| unambiguous semidirect product | C23⋊(C5×Dic11) |
| derived, Hall | C11×C23 ⋊ C4×C5 |
| Hall | C5×C11×C23 ⋊ C4 |
| Hall | C5×C23 ⋊ Dic11 |
| Hall | C5×C11 ⋊ Dic23 |
| Sylow | C23 ⋊ C5×Dic11 |
| Sylow | C11 ⋊ C5×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D253 |
| commutator, hypocenter | C11×C23 | C4×C5 |
| Frattini | C2 | C5×D253 |
| Fitting, socle | C2×C5×C11×C23 | C2 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic253, C5×Dic759, C25×Dic253, … |
| maximal normal subgroup of | C3×C5×Dic253, C25×Dic253, C23⋊(Dic11⋊C25), … |
| maximal quotient of | C3×C5×Dic253, C5×Dic759, C25×Dic253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5060, 6);