Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D157⋊#131 |
| Sylow | C157 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,e^2=f,g^a=g^129,c^b=cf,g^d=g^156,g^e=g^156430 conjugacy classes — view the full character table.
| maximal subgroup of | #34115912, #34115916, #34116175, … |
| maximal normal subgroup of | #34115912, #34115916, #34116175, … |
| maximal quotient of | #34116696, C4×#19097858, C4×#19097859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1625);