Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2151 |
160 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,c^b=cg,h^c=h^781616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2151×D79, C2×#23765157, #34441254, … |
| maximal normal subgroup of | #2151×D79, C2×#23765157, #34441254, … |
| maximal quotient of | #34199815, #34199841, #34199874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6267);