Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C107 ⋊ C2 |
| Sylow | C107 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^106,c^b=ce,g^b=g^1061724 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D107, C2×#20292356, #28334842, … |
| maximal normal subgroup of | D4⋊C8×D107, C2×#20292356, #28334842, … |
| maximal quotient of | #28334281, #28334283, #28334301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 278);