Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #350×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^78,d^b=df,f^b=fg,h^b=h^78,e^c=eg1115 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2195×D79, C2×#23765380, #34442220, … |
| maximal normal subgroup of | #2195×D79, C2×#23765380, #34442220, … |
| maximal quotient of | #34200424, #34200430, #34200768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6490);