Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C433 ⋊ C2 |
| Sylow | C433 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3464 |
Polycyclic presentation:
2^5,433|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^432,d^b=de,f^c=f^4321523 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D433, C2×#28357247, #42122608, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D433, C2×#28357247, #42122608, … |
| maximal quotient of | #42121811, #42121814, #42121850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 173);