Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×#120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#379⋊C3 |
| unambiguous semidirect product | (D3×#379)⋊C3 |
| Fitting | C3×#379 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C2×C3×C4 |
1281 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 1281 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AΣL(1,𝔽64), D3×#1020⋊C4, D3×#72991, … |
| maximal normal subgroup of | D3×AΣL(1,𝔽64), D3×#1020⋊C4, D3×#72991, … |
| maximal quotient of | C2×D3×#379⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155154);