Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | D9×#535 |
| Fitting | C9×#535 ⋊ C2 |
| Sylow | C9 ⋊ C2×#535 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C9×#535 | C2 |
| hypercenter | #535 | D9 |
| hypocenter | C9 | C2×#535 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ #535 | |
2844 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3498, D9×#3484, AGL(1,ℤ/9)×#535 |
| maximal normal subgroup of | D9×#3498, D9×#3484, AGL(1,ℤ/9)×#535 |
| maximal quotient of | D9×#2433, D9×#2669 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134989);