Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C157 ⋊ C2 |
| Sylow | C157 ⋊ #556 |
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^156,g^c=g^1561117 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34112046, #34112048, #34112068, … |
| maximal normal subgroup of | #34112046, #34112048, #34112068, … |
| maximal quotient of | #34103028, #34103031, #34103080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1270);