Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#71266 |
| Fitting | C32×#492 ⋊ C2 |
| Sylow | C32 ⋊ #1629 |
699 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 699 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10771251, #72219780, #72219782 |
| maximal normal subgroup of | C3×#10771251, #72219780, #72219782 |
| maximal quotient of | C3×#10708944, C3×#10708954 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 13303);