Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#6039 |
| Hall | C3×C52 ⋊ C2×Q8 |
| Sylow | C52 ⋊ D3×Q8 |
| Sylow | C3 ⋊ C2×#6039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D52 |
| commutator, Fitting, socle, cosocle | C2×C3×C52 | C23 |
| prime radical | C2×C52×D3 | C22 |
| hypocenter | C3×C52 | C2×Q8 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
184 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87872, D3×#87880, D3×#87873, … |
| maximal normal subgroup of | D3×#87872, D3×#87880, D3×#87873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 642);