Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×#3874 |
| Fitting | C52×C8 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C8 |
| Sylow | C52 ⋊ D3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #3874 |
| commutator, hypocenter | C52⋊C3 | C2×C8 |
| Frattini | C4 | C2×#3874 |
| Fitting | C52×C8 | D3 |
| socle | C2×C52 | C4×D3 |
| prime radical | C2×#3874 | C4 |
| cosocle | C4×C52⋊C3 | C22 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C8 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 229);