Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C433 ⋊ C4 |
| Sylow | C433 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3464 |
Polycyclic presentation:
2^5,433|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^179,c^b=ce,f^b=f^432,f^d=f^432554 conjugacy classes — view the full character table.
| maximal subgroup of | D433⋊#104, C2×#28357285, #42122808, … |
| maximal normal subgroup of | D433⋊#104, C2×#28357285, #42122808, … |
| maximal quotient of | #42122659, Q8⋊#16812365, #42122663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 211);