Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C107 ⋊ C2 |
| Sylow | C107 ⋊ #510 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^106,d^b=de,e^b=ef,g^c=g^106599 conjugacy classes — view the full character table.
| maximal subgroup of | #510×D107, C2×#20293069, #28349594, … |
| maximal normal subgroup of | #510×D107, C2×#20293069, #28349594, … |
| maximal quotient of | #28338172, #28338179, #28338246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 991);