Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | #99×#157 |
| Fitting | C32×#99 ⋊ C4 |
| Sylow | C32 ⋊ C4×#99 |
622 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #99×PSU(3,𝔽2), #157×B(4,𝔽2), #72242749, … |
| maximal normal subgroup of | #99×PSU(3,𝔽2), #157×B(4,𝔽2), #72242749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17768);