Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C107 ⋊ C2 |
| Sylow | C107 ⋊ #459 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^106,e^c=ef1079 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28335515, #28335517, #28335526, … |
| maximal normal subgroup of | #28335515, #28335517, #28335526, … |
| maximal quotient of | #28335802, #28335816, #28335826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 744);