Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C449 ⋊ C4 |
| Sylow | C449 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3592 |
Polycyclic presentation:
2^5,449|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^67,c^b=ce,f^d=f^448574 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#28385402, #43272997, #43272998, … |
| maximal normal subgroup of | C2×#28385402, #43272997, #43272998, … |
| maximal quotient of | D4⋊#16813318, #43272855, #43272858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 208);