Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×C3×#5244 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2485 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 2485 conjugacy classes of subgroups — too many to draw. Only its 330 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×D3×B(4,𝔽2), AGL(1,𝔽7)×#5244, C2×#13143663 |
| maximal normal subgroup of | C2×C3×D3×B(4,𝔽2) |
| maximal quotient of | AGL(1,𝔽7)×#5244, C2×#13143663 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99260);