Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2185 |
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^78,d^b=df,f^b=fg1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34200381, #34200382, #34200392, … |
| maximal normal subgroup of | #34200381, #34200382, #34200392, … |
| maximal quotient of | #34200371, #34200715, #34201475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6427);