Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
| direct product | D12×C5⋊D5 |
| Fitting | C3×C4×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×D12 |
| Sylow | C3 ⋊ D4×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×C5⋊D5 |
| commutator, socle, cosocle | C2×C3×C52 | C23 |
| Fitting | C3×C4×C52 | C22 |
| hypercenter | C4 | D3×C5⋊D5 |
| hypocenter | C3×C52 | C2×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 ◁ C4 | |
432 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 300 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D12×C5⋊D5, D3×D4×C5⋊D5, #72229531, … |
| maximal normal subgroup of | C2×D12×C5⋊D5, D3×D4×C5⋊D5, #72229531, … |
| maximal quotient of | C2×D12×C5⋊D5, C5⋊D5×#626, C5⋊D5×C4⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 814);