Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D52⋊C2 |
| unambiguous semidirect product | D52⋊(C22×C3) |
| Fitting, socle | C2×C3×C52 ⋊ D4 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D52⋊C2 |
| commutator, cosocle | C5⋊D5 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | D4 |
| hypocenter | C52 | C2×C3×D4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C2×C3 | |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1001);