Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C107 ⋊ C2 |
| Sylow | C107 ⋊ #486 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^1061718 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28335552, #28335553, #28335559, … |
| maximal normal subgroup of | #28335552, #28335553, #28335559, … |
| maximal quotient of | #28336589, #28337144, #28337267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 896);