Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C157 ⋊ #397 |
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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=e,c^2=d,b^a=bd,c^a=ce,g^a=g^156,c^b=cf1582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #397×D157, C2×#23757201, #34103378, … |
| maximal normal subgroup of | #397×D157, C2×#23757201, #34103378, … |
| maximal quotient of | #34098379, #34098383, #34098385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 477);