Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#11925896 |
| Fitting, socle | C2×C3×C112 ⋊ C2×C5 |
| derived, Sylow | C112 ⋊ C22×C3×C5 |
| Hall | C3×#10597245 ⋊ C22 |
| Hall | C2×C3×C11×D11 ⋊ C5 |
| Hall | #10597245 ⋊ C22×C3 |
| Hall | C2×C11×D11 ⋊ C3×C5 |
| Hall | C3×C112 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #11925896 |
| commutator, hypocenter | C112 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C3 | |
84 conjugacy classes of subgroups.
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 153);