Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #3874⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10597077 |
| derived, Hall | C52⋊C3 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #3874⋊C2 |
| commutator, hypocenter | C52⋊C3 | C22×C4 |
| Frattini | C2 | C2×#3874⋊C2 |
| Fitting, socle | C22×C52 | C2×D3 |
| prime radical | C22×#3874 | C2 |
| cosocle | C2×C52⋊C3 | C23 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C22 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 516);