Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #23363 |
664 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=e,c^2=ef,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=def,i^a=i^10,c^b=cef,d^b=de,i^g=i^27,i^h=i^72202 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1118240);