Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C107 ⋊ #359 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^106,c^b=ce,e^b=ef764 conjugacy classes — view the full character table.
| maximal subgroup of | #359×D107, C2×#20292434, #28338187, … |
| maximal normal subgroup of | #359×D107, C2×#20292434, #28338187, … |
| maximal quotient of | #28334422, #28334425, #28334476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 356);