Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C157 ⋊ C2 |
| Sylow | C157 ⋊ #360 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^156,c^b=cef,d^b=df,e^b=ef,g^b=g^1561576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #360×D157, C2×#23757084, #34101870, … |
| maximal normal subgroup of | #360×D157, C2×#23757084, #34101870, … |
| maximal quotient of | #34098104, #34098107, #34098146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 360);