Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D4⋊C8×C73 ⋊ C4 |
| Sylow | C73 ⋊ #8192 |
514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=e,d^2=g,e^2=h,b^a=bd,d^a=dg,f^a=fg,i^a=i^27,c^b=ch,i^b=i^46,i^c=i^27,i^e=i^72,i^f=i^72580 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1087188);