Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C79 ⋊ #1720 |
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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=dfg,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^78,c^b=cf,h^b=h^78884 conjugacy classes — view the full character table.
| maximal subgroup of | #1720×D79, C2×#23763062, #34276037, … |
| maximal normal subgroup of | #1720×D79, C2×#23763062, #34276037, … |
| maximal quotient of | #34182066, #34188050, #34188053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4172);