Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14579261 |
| Sylow | C317 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,d^2=e,b^a=bc,f^a=f^3162548 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35202946, #35202947, #35202948, … |
| maximal normal subgroup of | #35202946, #35202947, #35202948, … |
| maximal quotient of | #35202947, #35202949, D4⋊#14579261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 59);