Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C157 ⋊ C4 |
| Sylow | C157 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^129,d^b=de,g^b=g^156,d^c=df,g^d=g^156403 conjugacy classes — view the full character table.
| maximal subgroup of | D157⋊AΣL(1,𝔽16), C2×#23758174, #34116389, … |
| maximal normal subgroup of | D157⋊AΣL(1,𝔽16), C2×#23758174, #34116389, … |
| maximal quotient of | #34115061, #34115080, #34115115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1450);