Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C113 ⋊ C8 |
| Sylow | C113 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 904 |
Polycyclic presentation:
2^7,113|a^2=d,b^2=e,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^44,h^b=h^18,h^d=h^15,h^e=h^98,h^g=h^112196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 21517);