Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #106×C157 ⋊ C2 |
| Sylow | C157 ⋊ #485 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=f,b^2=f,c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^156,g^b=g^156,e^c=ef,g^c=g^1561111 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #485×D157, C2×#23757617, #34110046, … |
| maximal normal subgroup of | #485×D157, C2×#23757617, #34110046, … |
| maximal quotient of | #34100230, #34100334, #34100447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 893);