Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×#1220 |
| Fitting | C23×C3×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×#67 |
| Sylow | C3 ⋊ C2×C5×C22⋊D5 |
280 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11925664, C2×C3×C5×#1220, C2×C5×D3×C22⋊D5, … |
| maximal normal subgroup of | C2×#11925664, C2×C3×C5×#1220, C2×C5×D3×C22⋊D5, … |
| maximal quotient of | C2×C3×C5×#1220, C5×#91821, C2×C5×#67184 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 924);