Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C179 ⋊ #388 |
190 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 75 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^2=df,c^2=d,b^a=bd,c^a=ce,g^a=g^178,g^b=g^1781808 conjugacy classes. The character table is too large to display.
| maximal quotient of | #37507225, #37507234, #37507237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 442);