Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#10589323 |
| Sylow | C32 ⋊ C2×#334 |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11772179, C2×C3⋊D3×#334, C2×#11772176, … |
| maximal normal subgroup of | C2×#11772179, C2×C3⋊D3×#334, C2×#11772176, … |
| maximal quotient of | C2×#11772179, C2×#11772193 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 10766);