Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #64480⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#64480⋊C2 |
| unambiguous semidirect product | #64480⋊C22 |
| unambiguous semidirect product | (#1043⋊C3)⋊C22 |
| unambiguous semidirect product | (#3874⋊C2)⋊C4 |
| Fitting, socle | C2×C52 ⋊ C4×D3 |
| derived, Hall | C52⋊C3 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #64480⋊C2 |
| commutator, hypocenter | C52⋊C3 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | C4×D3 |
| prime radical | C2×#3874⋊C2 | C2 |
| cosocle | (C5⋊D5)⋊C3 | C23 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 951);