Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C3×C5×C112 ⋊ C22 |
| Hall | C5×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D5 |
| Sylow | C112 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ D112 |
| Sylow | C5 ⋊ D33⋊D11 |
| Sylow | C3 ⋊ D55⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C112 | C22 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11^2|c^a=c^2,d^a=d^4,e^a=e^10,e^b=e^10,f^b=f^10483 conjugacy classes — view the full character table.
| maximal subgroup of | ((C11⋊D11)⋊C9)⋊D5, #36344937, ((C11⋊D11)⋊C3)⋊D15, … |
| maximal normal subgroup of | C3×#20300106, ((C11⋊C5)⋊D11)⋊D15, #49137472, … |
| maximal quotient of | #36344937, C3×#20300106, #36345336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 206);