Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C2×C32×C5×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C2×C32×C31)⋊C52 |
| unambiguous semidirect product | (C2×C32×C5×C31)⋊C5 |
| Fitting, socle | C2×C32×C5×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C2×C32×C52 |
| Hall | C2×C32×C31 ⋊ C52 |
| Hall | C32×C31 ⋊ C2×C52 |
| Hall | C2×C31 ⋊ C32×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C2×C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C32×C5 | |
192 conjugacy classes of subgroups.
990 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 144);