Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C4×#64083 |
| Fitting | C32×C43 ⋊ C2 |
| Sylow | C32 ⋊ C4×#127 |
2772 conjugacy classes of subgroups; only the 649 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 649 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C3⋊D3×#127, AGL(1,𝔽5)×#64083, C4×#10590397 |
| maximal normal subgroup of | C4×C3⋊D3×#127, C4×#10590397 |
| maximal quotient of | AGL(1,𝔽5)×#64083 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36536);