Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#16812365 |
| Sylow | C433 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13856 |
Polycyclic presentation:
2^5,433|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^179,f^d=f^432884 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#16812365, #42122659, Q8⋊#16812365, … |
| maximal normal subgroup of | D4⋊#16812365, #42122659, Q8⋊#16812365, … |
| maximal quotient of | #42122672, #42122674, #42122677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 212);