Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C179 ⋊ #477 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=df,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^178,e^c=ef1799 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37508121, #37508123, #37508127, … |
| maximal normal subgroup of | #37508121, #37508123, #37508127, … |
| maximal quotient of | #37509005, #37509254, #37509592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 844);