Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C179 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^178,c^b=cf,g^b=g^1781802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37509210, #37509211, #37509215, … |
| maximal normal subgroup of | #37509210, #37509211, #37509215, … |
| maximal quotient of | #37507753, #37507768, #37507786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 592);