Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q32×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2251 |
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^c=h^78884 conjugacy classes — view the full character table.
| maximal subgroup of | #2251×D79, C2×#23765668, #34443690, … |
| maximal normal subgroup of | #2251×D79, C2×#23765668, #34443690, … |
| maximal quotient of | #34202941, #34202943, #34202950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6778);