Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | #100×#157 |
| Fitting | C32×#100 ⋊ C4 |
| Sylow | C32 ⋊ C4×#100 |
546 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 546 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 | #100×PSU(3,𝔽2), #157×#453, #72227609 |
| maximal normal subgroup of | #100×PSU(3,𝔽2), #157×#453, #72227609 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17794);