Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4×#1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | A4×#1044 |
| unambiguous semidirect product | (C22×#1044)⋊C3 |
| Fitting, socle, derived | C22×C52 ⋊ C3×C4 |
| Hall | C22×#1044 ⋊ C3 |
| Sylow | C52 ⋊ C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C52 | C3×C4 |
| prime radical | A4×C5⋊D5 | C2 |
| cosocle | C22×C5⋊D5 | C2×C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | #72213670, A4×D5⋊AGL(1,𝔽5), S4×#1044, … |
| maximal normal subgroup of | A4×D5⋊AGL(1,𝔽5), S4×#1044, #72213957, … |
| maximal quotient of | #72213670, C22⋊A4×#1044, C2×A4×#1044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 977);