Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #99×C179 ⋊ C2 |
| Sylow | C179 ⋊ #458 |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 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.
Polycyclic presentation:
2^6,179|a^2=f,b^a=bd,c^a=ce,g^a=g^178,e^b=ef,d^c=df,g^c=g^178995 conjugacy classes — view the full character table.
| maximal subgroup of | #37510992, #37510993, #37510997, … |
| maximal normal subgroup of | #37510992, #37510993, #37510997, … |
| maximal quotient of | #37507987, #37507988, #37507992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 740);