Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D5×C22⋊D5 |
| Fitting | C22×C3×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×D52 |
| commutator, cosocle | C2×C52 | C23×C3 |
| Frattini | C2 | C2×C3×D52 |
| Fitting | C22×C3×C52 | C22 |
| socle | C2×C3×C52 | C23 |
| hypercenter | C22×C3 | D52 |
| hypocenter | C52 | C2×C3×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3 | |
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D4×D52, C3×#11925663, D3×D5×C22⋊D5, … |
| maximal normal subgroup of | C3×D4×D52, D3×D5×C22⋊D5, D5×#6790, … |
| maximal quotient of | C3×#11925663 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 774);