Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16812358 |
| 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^4323476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42121534, #42121535, #42121536, … |
| maximal normal subgroup of | #42121534, #42121535, #42121536, … |
| maximal quotient of | #42121535, #42121537, D4⋊#16812358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 59);