Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D9×B(4,𝔽2) |
| Fitting | C9×B(4,𝔽2) ⋊ C2 |
| Sylow | C9 ⋊ C2×B(4,𝔽2) |
1527 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 1527 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×B(4,𝔽2), #72220167, D9×#5934, … |
| maximal normal subgroup of | AGL(1,ℤ/9)×B(4,𝔽2), C2×D9×B(4,𝔽2), D9×#3026 |
| maximal quotient of | #72220167, C2×D9×B(4,𝔽2), #72268822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99252);