Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C179 ⋊ #353 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^178,c^b=cf,d^b=def,d^c=df1259 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507145, #37507146, #37507162, … |
| maximal normal subgroup of | #37507145, #37507146, #37507162, … |
| maximal quotient of | #37506932, #37506946, #37506997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 342);