Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16812365 |
| Sylow | C433 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^5,433|a^2=d,d^2=e,b^a=bc,f^a=f^179,f^d=f^432884 conjugacy classes — view the full character table.
| maximal subgroup of | #42122654, #42122655, #42122656, … |
| maximal normal subgroup of | #42122654, #42122655, #42122656, … |
| maximal quotient of | #42122654, #42122656, D4⋊#16812365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 202);