Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C433 ⋊ C4 |
| Sylow | C433 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3464 |
Polycyclic presentation:
2^5,433|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^179,c^b=ce,f^d=f^432554 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#28357282, #42122801, #42122802, … |
| maximal normal subgroup of | C2×#28357282, #42122801, #42122802, … |
| maximal quotient of | D4⋊#16812365, #42122659, #42122662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 208);