Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of S4×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | S4×D25 |
| unambiguous semidirect product | (S4×C25)⋊C2 |
| unambiguous semidirect product | (A4⋊D25)⋊C2 |
| unambiguous semidirect product | (A4×D25)⋊C2 |
| Fitting | C22×C25 ⋊ C2×D3 |
| derived | A4×C25 ⋊ C22 |
| Sylow | C25 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C25 | C22 |
| Frattini | C5 | D5×S4 |
| Fitting | C22×C25 | C2×D3 |
| socle | C22×C5 | D3×D5 |
| LCS | G ▷ A4×C25 | |
| UCS | C1 | |
99 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 100 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D25⋊C5, S4×#1035 |
| maximal normal subgroup of | S4×D25⋊C5, S4×#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 195);