Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊Q8×C107 ⋊ C2 |
| Sylow | C107 ⋊ #456 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^106,d^c=df758 conjugacy classes — view the full character table.
| maximal subgroup of | #28334614, #28334616, #28338482, … |
| maximal normal subgroup of | #28334614, #28334616, #28338482, … |
| maximal quotient of | #28335422, #28335429, #28335434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 731);