Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6714 |
| Fitting | C2×C3×C4×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C5×#685 |
168 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72259975, C5×D3×#685, #72260133 |
| maximal normal subgroup of | #72259975, C5×D3×#685, #72260133 |
| maximal quotient of | C5×#91089 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 443);