Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C317 ⋊ C4 |
| Sylow | C317 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^203,c^b=ce,f^b=f^316,f^d=f^316409 conjugacy classes — view the full character table.
| maximal subgroup of | D317⋊#104, C2×#23778845, #35204220, … |
| maximal normal subgroup of | D317⋊#104, C2×#23778845, #35204220, … |
| maximal quotient of | #35204071, Q8⋊#14579268, #35204075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 211);