Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #324×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1615 |
208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 208 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=fg,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^78,d^b=df,e^b=eg,h^b=h^78,d^c=dg881 conjugacy classes — view the full character table.
| maximal subgroup of | #1615×D79, C2×#23762433, #34260423, … |
| maximal normal subgroup of | #1615×D79, C2×#23762433, #34260423, … |
| maximal quotient of | #34177301, #34177308, #34177376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3543);