Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29×C3 |
| direct product | C3⋊D3×#379 |
| Fitting | C32×#379 ⋊ C2 |
| Sylow | C32 ⋊ C2×#379 |
10392 conjugacy classes of subgroups; only the 625 normal subgroups are shown.
This group has 10392 conjugacy classes of subgroups — too many to draw. Only its 625 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1889, C3⋊D3×#2846, C3⋊D3×#1781, … |
| maximal normal subgroup of | C3⋊D3×#1889, C3⋊D3×#2846, C3⋊D3×#1781, … |
| maximal quotient of | C3⋊D3×#1781, C3⋊D3×#1438, C3⋊D3×#65800 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34964);