Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×C3×C4×D3×D4 |
| Fitting | C2×C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C22×C4×D4 |
5269 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D32×D4, C2×C3×D3×#442 |
| maximal normal subgroup of | C2×C4×D32×D4, C2×C3×D3×#442 |
| maximal quotient of | C3×#11659463, C3×#11659527, C2×C3×D3×#442 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133884);