Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14579268 |
| Sylow | C317 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^203,f^d=f^316652 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14579268, #35204071, Q8⋊#14579268, … |
| maximal normal subgroup of | D4⋊#14579268, #35204071, Q8⋊#14579268, … |
| maximal quotient of | #35204084, #35204086, #35204089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 212);