Finite Group DatabasebetaFinite Group Databasebeta| order | 9156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #17987079⋊C2 |
| unambiguous semidirect product | #17987083⋊C2 |
| unambiguous semidirect product | #17987087⋊C2 |
| Fitting, socle, derived, Hall | C7×C109 ⋊ C22×C3 |
| Hall | D7×D109 ⋊ C3 |
| Hall | #14556233 ⋊ C22 |
| Sylow | C109 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×D109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C109 | C22×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,109|e^a=e^108,d^b=d^6,d^c=d^2,e^c=e^45104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D109⋊C3, C3×#17987079⋊C2, #17987079⋊D3, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D109⋊C3, C3×#17987079⋊C2 |
| maximal quotient of | #28351522⋊C2, C3×#17987079⋊C2, #17987079⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9156, 30);