Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q8×C113 ⋊ C8 |
| Sylow | C113 ⋊ #1479 |
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1808 |
Polycyclic presentation:
2^7,113|a^2=e,b^2=f,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^18,c^b=cf,d^b=df,h^e=h^98,h^g=h^112184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 21631);