Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#16813320 |
| Fitting | C4×C449 ⋊ C8 |
| Sylow | C449 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1796 |
Polycyclic presentation:
2^5,449|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^122,f^d=f^67,f^e=f^448244 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#16813320, Q8⋊#16813320, #43273096, … |
| maximal normal subgroup of | D4⋊#16813320, Q8⋊#16813320, #43273096, … |
| maximal quotient of | #43273096, #43273097, (C2×#16813320)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 239);