Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #490×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1657 |
206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|c^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,h^b=h^78,d^c=dg,e^c=efg644 conjugacy classes — view the full character table.
| maximal subgroup of | #1657×D79, C2×#23762697, #34269421, … |
| maximal normal subgroup of | #1657×D79, C2×#23762697, #34269421, … |
| maximal quotient of | #34176977, #34176988, #34177000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3807);