Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C317 ⋊ C4 |
| Sylow | C317 ⋊ #97 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^203,f^d=f^316652 conjugacy classes — view the full character table.
| maximal subgroup of | #35204113, #35204114, C2×#23778834, … |
| maximal normal subgroup of | #35204113, #35204114, C2×#23778834, … |
| maximal quotient of | #35204064, #14579268⋊C8, (C2×#11929639)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 200);