Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C73 ⋊ #21798 |
1386 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^27,c^b=ce,g^c=gh,i^d=i^72,i^g=i^72556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1107372);