Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #1043⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#6033⋊C3 |
| unambiguous semidirect product | (C2×#6033)⋊C3 |
| derived, Sylow | C52 ⋊ C2×C3×C8 |
| Hall | C2×#6033 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #1043⋊C3 |
| commutator, hypocenter | C52 | C2×C3×C8 |
| Frattini | C2 | C2×#1043⋊C3 |
| Fitting, socle | C22×C52 | C3×C4 |
| prime radical | C22×C52⋊C3 | C4 |
| cosocle | #1039 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 503);