Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C22⋊ΓL(1,𝔽8)×C43⋊C3 |
| unambiguous semidirect product | (C22×C43⋊C3)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C7×C43⋊C3)⋊A4 |
| Fitting, socle, derived, Hall | C22×C7×C43 ⋊ C32 |
| Hall | C7×C43 ⋊ C3×A4 |
| Hall | C22×C43 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C43 ⋊ C3×C22⋊ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C3×C43⋊C3 |
| Sylow | C7 ⋊ A4×C43⋊C3 |
| Sylow | C22 ⋊ ΓL(1,𝔽8)×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C7×C43 | C32 |
| LCS | G ▷ C22×C7×C43 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 193);