Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×C52×D12 |
| Fitting | C2×C3×C4×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C3 ⋊ C2×C52×D4 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D12×C5⋊D5, C2×C52×D3×D4, C2×#11925606, … |
| maximal normal subgroup of | C2×D12×C5⋊D5, C2×C52×D3×D4, C2×#11925606, … |
| maximal quotient of | C52×#874, C2×C52×C4⋊(C3⋊D3), C2×C52×#626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 907);