Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C179 ⋊ #357 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^178,c^b=ce,e^b=ef1268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D179, C2×#26038240, #37510704, … |
| maximal normal subgroup of | #357×D179, C2×#26038240, #37510704, … |
| maximal quotient of | #37506961, #37507009, #37507046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 350);