Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C107 ⋊ #339 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^1061724 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #339×D107, C2×#20292387, #28336169, … |
| maximal normal subgroup of | #339×D107, C2×#20292387, #28336169, … |
| maximal quotient of | #28334294, #28334298, #28334301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 309);