Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C317 ⋊ C4 |
| Sylow | C317 ⋊ #117 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=e,c^2=d,b^a=bd,f^a=f^203,f^e=f^316652 conjugacy classes — view the full character table.
| maximal subgroup of | #35204090, #35204091, #35204094, … |
| maximal normal subgroup of | #35204090, #35204091, #35204094, … |
| maximal quotient of | #35204159, C4×C22⋊#11929639, C4×C4⋊#11929639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 225);