Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C157 ⋊ C4 |
| Sylow | C157 ⋊ #520 |
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|a^2=f,d^2=e,b^a=be,d^a=de,g^a=g^129,c^b=ce,g^f=g^156424 conjugacy classes — view the full character table.
| maximal subgroup of | #34116095, #34116096, #34116135, … |
| maximal normal subgroup of | #34116095, #34116096, #34116135, … |
| maximal quotient of | #34116573, #34116575, #34116576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1618);