Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C7×#1517 ⋊ C2 |
| Sylow | C7 ⋊ #18309 |
1168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=gh,d^2=h,e^2=g,b^a=be,c^a=cf,d^a=dh,e^a=eg,i^a=i^6,e^b=eg,f^b=fh,e^c=eh,i^c=i^6136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 143615);