Finite Group DatabasebetaFinite Group Databasebeta| order | 1550 |
| isoclinism | isoclinic class of D31⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D31⋊C5 |
| unambiguous semidirect product | D31⋊C52 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D31)⋊C5 |
| Fitting, socle | C5×C31 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C52 |
| Hall | C5×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D31 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 155 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D31⋊C5, C2×C5×D31⋊C5, C5×AGL(1,𝔽31), … |
| maximal normal subgroup of | D5×D31⋊C5, C2×C5×D31⋊C5, C5×AGL(1,𝔽31), … |
| maximal quotient of | C5×Dic31⋊C5, C2×C5×D31⋊C5, C3×C5×D31⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1550, 7);