Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C23×C5 |
| direct product | C52×D3×D4 |
| Fitting | C3×C52×D4 ⋊ C2 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C3 ⋊ C2×C52×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C52 | C22×D3 |
| commutator, cosocle | C2×C3 | C23×C52 |
| Frattini | C2 | C22×C52×D3 |
| Fitting | C3×C52×D4 | C2 |
| socle | C2×C3×C52 | C23 |
| hypercenter | C52×D4 | D3 |
| hypocenter | C3 | C2×C52×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C52 ◁ C52×D4 | |
432 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 300 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C52×D3×D4, D3×D4×C5⋊D5, C52×D4×C3⋊D3, … |
| maximal normal subgroup of | C2×C52×D3×D4, D3×D4×C5⋊D5, C5×D3×#687, … |
| maximal quotient of | C2×C52×D3×D4, C52×#937, C52×D4×C3⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 909);