Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C4×#120⋊C3 |
| unambiguous semidirect product | (C4×#120)⋊C32 |
| unambiguous semidirect product | (C3×C4×#120)⋊C3 |
| Fitting | C3×C4×#120 ⋊ C3 |
| derived | C24 ⋊ C2×C32×C4 |
| Sylow | C4×#120 ⋊ C32 |
568 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×#1020⋊C2, C4×D3×#120⋊C3, C4×#10593630 |
| maximal normal subgroup of | C3×C4×#1020⋊C2, C4×D3×#120⋊C3, C4×#10593630 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153423);