Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | #127×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×#127 |
2772 conjugacy classes of subgroups; only the 709 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 709 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C3⋊D3×#127, #127×C3⋊ΓL(1,𝔽16), #72259840 |
| maximal normal subgroup of | C4×C3⋊D3×#127, #72259840 |
| maximal quotient of | #127×C3⋊ΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36539);