Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×#10624391 |
| Fitting, socle | C2×C5×C112 ⋊ D3 |
| derived, Hall | C112⋊C3 ⋊ C22×C5 |
| Hall | C5×C112⋊C3 ⋊ C22 |
| Hall | C5×C112 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #10624391 |
| commutator, hypocenter | C112⋊C3 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C112 | D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C2×C5 | |
64 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 174);