Finite Group DatabasebetaFinite Group Databasebeta| order | 7460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D373 |
| unambiguous semidirect product | (D5×C373)⋊C2 |
| unambiguous semidirect product | (C5×D373)⋊C2 |
| unambiguous semidirect product | D1865⋊C2 |
| Fitting, socle, derived, Hall | C5×C373 ⋊ C22 |
| Sylow | C373 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D373 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C373 | C22 |
| LCS | G ▷ C5×C373 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
752 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D373⋊C3, C3×D5×D373, D15×D373, … |
| maximal normal subgroup of | D5×D373⋊C3, C3×D5×D373, C5×D5×D373 |
| maximal quotient of | C3×D5×D373, D15×D373, D5×D1119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7460, 12);