Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #1830 |
236 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 73 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=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^78,e^c=eg887 conjugacy classes — view the full character table.
| maximal subgroup of | #1830×D79, C2×#23763513, #34288137, … |
| maximal normal subgroup of | #1830×D79, C2×#23763513, #34288137, … |
| maximal quotient of | #34181730, #34181736, #34181790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4623);