Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C317 ⋊ C2 |
| Sylow | C317 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^316,d^b=de,f^c=f^3161117 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D317, C2×#23778807, #35204020, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D317, C2×#23778807, #35204020, … |
| maximal quotient of | #35203223, #35203226, #35203262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 173);