Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C73 ⋊ C4 |
| Sylow | C73 ⋊ #13804 |
1662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=h,c^2=ef,d^2=e,b^a=be,c^a=cf,i^a=i^27,d^b=de,i^g=i^72820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1098276);