Finite Group DatabasebetaFinite Group Databasebeta| order | 1550 |
| isoclinism | isoclinic class of D5×ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D5×ΓL(1,𝔽32) |
| unambiguous semidirect product | C5⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (D5×C31)⋊C5 |
| Fitting, socle, derived | C5×C31 ⋊ C2×C5 |
| Hall | C5×ΓL(1,𝔽32) ⋊ C2 |
| Sylow | C31 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C31 | C2×C5 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 155 |
44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1550, 8);