Finite Group DatabasebetaFinite Group Databasebeta| order | 8932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊AGL(1,𝔽29) |
| unambiguous semidirect product | (C11⋊#1181)⋊C7 |
| Fitting, socle, derived, Hall | C11×C29 ⋊ C4×C7 |
| Hall | C11×C29⋊C7 ⋊ C4 |
| Hall | C11⋊#1181 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic11 |
| Sylow | C29 ⋊ C7×Dic11 |
| Sylow | C11 ⋊ AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C29 | C4×C7 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,2,11,29|a^2=c,d^a=d^10,e^a=e^17,e^b=e^16,e^c=e^28109 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊AGL(1,𝔽29), C3⋊(C11⋊AGL(1,𝔽29)) |
| maximal normal subgroup of | C3×C11⋊AGL(1,𝔽29) |
| maximal quotient of | C3×C11⋊AGL(1,𝔽29), C3⋊(C11⋊AGL(1,𝔽29)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8932, 15);