Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C107 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,c^b=ce,g^b=g^1061088 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D107, C2×#20292357, #28334840, … |
| maximal normal subgroup of | Q8⋊C8×D107, C2×#20292357, #28334840, … |
| maximal quotient of | #28334283, #28334286, #28334300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 279);