Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#16812367 |
| Fitting | C4×C433 ⋊ C8 |
| Sylow | C433 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1732 |
Polycyclic presentation:
2^5,433|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^354,f^d=f^179,f^e=f^432236 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#16812367, Q8⋊#16812367, #42122900, … |
| maximal normal subgroup of | D4⋊#16812367, Q8⋊#16812367, #42122900, … |
| maximal quotient of | #42122900, #42122901, (C2×#16812367)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 239);