Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C107 ⋊ C2 |
| Sylow | C107 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^106,c^b=cf,d^b=df,g^b=g^1061082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28336430, #28336432, #28336835, … |
| maximal normal subgroup of | #28336430, #28336432, #28336835, … |
| maximal quotient of | #28334853, #28334879, #28334905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 555);