Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | #120×#157 |
| Fitting | C32×#120 ⋊ C4 |
| Sylow | C32 ⋊ C4×#120 |
1886 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #120×PSU(3,𝔽2), #120×GO+(4,𝔽2), #120×AGL(1,𝔽9), … |
| maximal normal subgroup of | #120×PSU(3,𝔽2), #120×GO+(4,𝔽2), #120×AGL(1,𝔽9), … |
| maximal quotient of | #157×#453, #157×B(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36000);