Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C5 |
| direct product | C2×A4×C5⋊D5 |
| unambiguous semidirect product | (C2×C5)⋊(D5×A4) |
| Fitting, socle | C23×C52 ⋊ C2×C3 |
| derived | C22×C52 ⋊ C22×C3 |
| Hall | C23×C5⋊D5 ⋊ C3 |
| Sylow | C52 ⋊ C22×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×C5⋊D5 |
| commutator, cosocle, hypocenter | C22×C52 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | C2×C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C2 | |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C22×A4×C5⋊D5, C2×A4×#1043, C2×S4×C5⋊D5, … |
| maximal normal subgroup of | C22×A4×C5⋊D5, C2×A4×#1043, C2×S4×C5⋊D5, … |
| maximal quotient of | C22×A4×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1014);