Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C8 |
| direct product | C3×#68050 |
| Fitting | C32×C82 ⋊ C2 |
| Sylow | C32 ⋊ #1455 |
465 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#1455, C3×#10784429, C3×#10784425, … |
| maximal normal subgroup of | C3×D3×#1455, C3×#10784429, C3×#10784425 |
| maximal quotient of | #72252897 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7700);