Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of S4×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22×C5 |
| direct product | S4×C5⋊D5 |
| unambiguous semidirect product | (C5×S4)⋊D5 |
| Fitting, socle | C22×C52 ⋊ C2×D3 |
| derived | C52×A4 ⋊ C22 |
| Sylow | C52 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52×A4 | C22 |
| Fitting, socle | C22×C52 | C2×D3 |
| LCS | G ▷ C52×A4 | |
| UCS | C1 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#1020, S4×#1043, D52×S4, … |
| maximal normal subgroup of | S4×#1043, D52×S4, S4×#1044, … |
| maximal quotient of | C5⋊D5×#1020, C2×S4×C5⋊D5, #72230228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 982);