Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C157 ⋊ C2 |
| Sylow | C157 ⋊ #576 |
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^156,d^c=df,g^d=g^156880 conjugacy classes — view the full character table.
| maximal subgroup of | #34111897, #34111899, #34111901, … |
| maximal normal subgroup of | #34111897, #34111899, #34111901, … |
| maximal quotient of | #34108660, #34108661, #34108735, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1353);