Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4×C5 |
| direct product | C4×#1039⋊C3 |
| unambiguous semidirect product | (C4×#1039)⋊C3 |
| derived, Sylow | C52 ⋊ C3×C42 |
| Hall | C4×#1039 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C3×C42 |
| Frattini | C22 | C2×(C5⋊D5)⋊C3 |
| Fitting | C2×C4×C52 | C2×C3 |
| socle, cosocle | C22×C52 | C22×C3 |
| prime radical | C22×C52⋊C3 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 251);