Finite Group DatabasebetaFinite Group Databasebeta| order | 5060 |
| isoclinism | isoclinic class of D253 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D253 |
| unambiguous semidirect product | (C2×C23)⋊(C5×D11) |
| Fitting, socle | C2×C5×C11×C23 ⋊ C2 |
| derived, Hall | C11×C23 ⋊ C22×C5 |
| Hall | C5×C11×C23 ⋊ C22 |
| Hall | C5×C23 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C5×D11 |
| Sylow | C11 ⋊ C2×C5×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D253 |
| commutator, hypocenter | C11×C23 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C23 | C2 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D253, C2×C5×D759, C2×C3×C5×D253, … |
| maximal normal subgroup of | C2×C3×C5×D253, C2×C23⋊(D11⋊C25), C2×C25×D253, … |
| maximal quotient of | C5×D3×D253, C2×C5×D759, C2×C3×C5×D253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5060, 45);