Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D3×#577⋊C3 |
| unambiguous semidirect product | (D3×#577)⋊C3 |
| Fitting | C3×#577 ⋊ C2×C3 |
708 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×GL(2,𝔽3)⋊A4, D3×#3585⋊C3, D3×#85469, … |
| maximal normal subgroup of | D3×#3585⋊C3, D3×#85469, D3×#85470 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157344);