Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3×C4 |
| direct product | C3⋊D3×#492 |
| Fitting | C32×#492 ⋊ C2 |
| Sylow | C32 ⋊ C2×#492 |
1968 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 297 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3151, #72214117, C3⋊D3×#1705, … |
| maximal normal subgroup of | C3⋊D3×#3151, #72214117, C3⋊D3×#1705, … |
| maximal quotient of | C3⋊D3×#1705, C3⋊D3×#1715 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108148);