Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11925895⋊D3 |
| Fitting, socle, derived, Hall | C3×C112 ⋊ C22×C5 |
| Hall | C3×#10597243 ⋊ C22 |
| Hall | D11×D33 ⋊ C5 |
| Hall | #10597243 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ #11925892⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C112 | C22×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,3,11^2|d^a=d^2,f^a=f^10,e^b=e^10,e^c=e^4,f^c=f^454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 107);