Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ #447 |
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,179|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^178,d^b=df,g^b=g^1781799 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507919, #37507920, #37507931, … |
| maximal normal subgroup of | #37507919, #37507920, #37507931, … |
| maximal quotient of | #37507920, #37507937, #37507988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 685);