Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×D3×C22⋊D5 |
| Fitting | C22×C3×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ D3×D4 |
| Sylow | C3 ⋊ C2×C5×C22⋊D5 |
280 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 280 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) = 60 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87886, C5×#10624236, C5×D3×#709, … |
| maximal normal subgroup of | D3×#87886, C5×D3×#709, D3×#87880, … |
| maximal quotient of | C5×#10624236, C5×D3×#687, C5×D3×#686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 801);