Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C449 ⋊ C2 |
| Sylow | C449 ⋊ D16 |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
Polycyclic presentation:
2^5,449|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^4481579 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D16×D449, C2×#28385281, #43272437, … |
| maximal normal subgroup of | D16×D449, C2×#28385281, #43272437, … |
| maximal quotient of | #43271807, #43271808, #43271832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 87);