Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C5⋊S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×C5⋊S5 |
| unambiguous semidirect product | (C2×C5)⋊S5 |
| unambiguous semidirect product | (C2×A5)⋊D5 |
| Fitting | C2×C5 ⋊ S5 |
| socle | C2×C5×A5 ⋊ C2 |
| derived | C5×A5 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊S5 |
| commutator, cosocle, hypocenter | C5×A5 | C22 |
| Frattini | C1 | G |
| Fitting | C2×C5 | S5 |
| socle | C2×C5×A5 | C2 |
| LCS | G ▷ C5×A5 | |
| UCS | C1 ◁ C2 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C5⋊S5, C2×D5×S5 |
| maximal normal subgroup of | C2×C3×C5⋊S5, C2×D5×S5 |
| maximal quotient of | C2×A5⋊Dic5, C2×C3×C5⋊S5, #72277296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 942);