Finite Group DatabasebetaFinite Group Databasebeta| order | 1932 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)⋊D23 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊D23 |
| unambiguous semidirect product | (C2×C23)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C2×D161)⋊C3 |
| Fitting, socle | C2×C7×C23 ⋊ C2×C3 |
| derived, Hall | C7×C23 ⋊ C22×C3 |
| Hall | C2×D161 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C23 ⋊ C22 |
| Sylow | C23 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×D23 |
| Sylow | C7 ⋊ C2×C3×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)⋊D23 |
| commutator, cosocle, hypocenter | C7×C23 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C23 | C2×C3 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 322 |
124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1932, 16);