Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×D9×#127 |
| Fitting | C2×C9×#127 ⋊ C2 |
| Sylow | C9 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini | C22×C3 | C24×D3 |
| Fitting | C2×C9×#127 | C2 |
| socle | C23×C3 | C23×D3 |
| hypercenter | C2×#127 | D9 |
| hypocenter | C9 | C22×#127 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
4500 conjugacy classes of subgroups; only the 766 normal subgroups are shown.
This group has 4500 conjugacy classes of subgroups — too many to draw. Only its 766 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3151, D9×#3498, C2×D9×#453, … |
| maximal normal subgroup of | D9×#3151, D9×#3498, C2×D9×#453, … |
| maximal quotient of | D9×#3151, D9×#2433, C22×D9×#127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134701);