Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#14272338 |
| Sylow | C233 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7456 |
Polycyclic presentation:
2^6,233|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^232,c^b=ce2348 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D233, C2×D4⋊#14272338, #44450189, … |
| maximal normal subgroup of | D4⋊C8×D233, C2×D4⋊#14272338, #44450189, … |
| maximal quotient of | #44449631, #44449633, #44449651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 277);