Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2064 |
208 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 65 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=de,b^2=d,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^78,c^b=cf,h^b=h^78,d^c=dg,f^c=fg,h^c=h^78884 conjugacy classes — view the full character table.
| maximal subgroup of | #2064×D79, C2×#23764768, #34316813, … |
| maximal normal subgroup of | #2064×D79, C2×#23764768, #34316813, … |
| maximal quotient of | #34192794, #34192808, #34192822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5878);