Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C157 ⋊ C4 |
| Sylow | C157 ⋊ #444 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^129,d^b=df,g^b=g^156,g^c=g^129,g^e=g^156295 conjugacy classes — view the full character table.
| maximal subgroup of | #34116543, #34116544, #34116547, … |
| maximal normal subgroup of | #34116543, #34116544, #34116547, … |
| maximal quotient of | #34115726, #34115729, #34115734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1595);