Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #102×C107 ⋊ C2 |
| Sylow | C107 ⋊ #490 |
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,107|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,c^b=cf,g^c=g^106758 conjugacy classes — view the full character table.
| maximal subgroup of | #490×D107, C2×#20292990, #28346803, … |
| maximal normal subgroup of | #490×D107, C2×#20292990, #28346803, … |
| maximal quotient of | #28336593, #28337155, #28337156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 912);