Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C215 |
| direct product | C23×C3×D3×D4 |
| Fitting | C23×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C3 | C22×D3 |
| commutator, cosocle | C2×C3 | C26×C3 |
| Frattini | C2 | C25×C3×D3 |
| Fitting | C23×C32×D4 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C23×C3×D4 | D3 |
| hypocenter | C3 | C24×C3×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C24×C3 ◁ C23×C3×D4 | |
21785 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D32×D4, C3×D3×#3484, C23×D4×AGL(1,ℤ/9) |
| maximal normal subgroup of | C23×D32×D4, C3×D3×#3484 |
| maximal quotient of | C3×D3×#3484, C3×D3×#3498, C23×D4×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153168);