Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of (C24⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×(C24⋊C5)⋊C2 |
| unambiguous semidirect product | (C24⋊C5)⋊(C2×C5) |
| Fitting, socle | C24×C5 ⋊ D5 |
| derived | C24⋊C5 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C24⋊C5)⋊C2 |
| commutator, cosocle, hypocenter | C24⋊C5 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C5 | D5 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C5 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#66297, #13107908, D5×(C24⋊C5)⋊C2, … |
| maximal normal subgroup of | C5×#66297, #13107908, D5×(C24⋊C5)⋊C2, … |
| maximal quotient of | C5×#66243, C5×#66244, C5×#66245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1195);