Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C449 ⋊ C2 |
| Sylow | C449 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3592 |
Polycyclic presentation:
2^5,449|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^448,d^b=de,f^c=f^4481579 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D449, C2×#28385367, #43272804, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D449, C2×#28385367, #43272804, … |
| maximal quotient of | #43272007, #43272010, #43272046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 173);