Finite Group DatabasebetaFinite Group Databasebeta| order | 9108 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊AGL(1,𝔽23) |
| unambiguous semidirect product | ((C3⋊D3)⋊D23)⋊C11 |
| unambiguous semidirect product | (C3⋊AGL(1,𝔽23))⋊D3 |
| Fitting, socle, derived, Hall | C32×C23 ⋊ C22×C11 |
| Hall | C32×C23⋊C11 ⋊ C22 |
| Hall | (C3⋊D3)⋊D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D32 |
| Sylow | C23 ⋊ D32×C11 |
| Sylow | C32 ⋊ C2×AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C23 | C22×C11 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11,3^2,23|e^a=e^2,f^a=f^22,d^b=d^2,e^b=e^2,f^c=f^2105 conjugacy classes — view the full character table.
| maximal subgroup of | D32×AGL(1,𝔽23) |
| maximal normal subgroup of | D32×AGL(1,𝔽23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9108, 57);