Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C107 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^1061082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28336669, #28336670, #28336674, … |
| maximal normal subgroup of | #28336669, #28336670, #28336674, … |
| maximal quotient of | #28335211, #28335226, #28335244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 589);