Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16813320 |
| unambiguous semidirect product | (C2×#16813320)⋊C2 |
| Fitting | C22×C449 ⋊ C8 |
| Sylow | C449 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1796 |
Polycyclic presentation:
2^5,449|a^2=d,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 | #43273092, #43273093, C2×C22⋊#16813320, … |
| maximal normal subgroup of | #43273092, #43273093, C2×C22⋊#16813320, … |
| maximal quotient of | #43273092, #43273093, D4⋊#16813320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 238);