Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C107 ⋊ C2 |
| Sylow | C107 ⋊ #454 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^106,d^b=df,e^b=ef,g^b=g^106,d^c=df599 conjugacy classes — view the full character table.
| maximal subgroup of | #28338479, #28338483, #28338488, … |
| maximal normal subgroup of | #28338479, #28338483, #28338488, … |
| maximal quotient of | #28335392, #28335398, #28335403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 724);