Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊(#120⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C3⋊(#120⋊C3) |
| unambiguous semidirect product | (C4×#953)⋊C3 |
| Fitting | C24×C3×C4 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C2×C3×C4 |
529 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 529 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#120⋊C3, C4×#10593244 |
| maximal normal subgroup of | C4×D3×#120⋊C3, C4×#10593244 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155367);