Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#5244 |
| Fitting | C32×H(5,𝔽2) ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2135 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 2135 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D32×B(4,𝔽2), #72252896, #72253276, … |
| maximal normal subgroup of | D32×B(4,𝔽2) |
| maximal quotient of | #72252896, D3×#10591531, #72258275 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99268);