Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C317 ⋊ M32 |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^203,f^b=f^316,f^c=f^316652 conjugacy classes — view the full character table.
| maximal subgroup of | #35204113, #35204114, #35204139, … |
| maximal normal subgroup of | #35204113, #35204114, #35204139, … |
| maximal quotient of | #35204112, #35204118, #35204144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 221);