Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C107 ⋊ #491 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=f,b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,c^b=cf,g^b=g^106,g^c=g^106758 conjugacy classes — view the full character table.
| maximal subgroup of | #28334633, #28335783, #28335788, … |
| maximal normal subgroup of | #28334633, #28335783, #28335788, … |
| maximal quotient of | #28336596, #28337154, #28337282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 917);