Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #1611 |
210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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=g,b^2=f,c^2=g,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^78,d^b=df,e^b=eg,d^c=dg,h^c=h^78764 conjugacy classes — view the full character table.
| maximal subgroup of | #1611×D79, C2×#23762409, #34260530, … |
| maximal normal subgroup of | #1611×D79, C2×#23762409, #34260530, … |
| maximal quotient of | #34177348, #34177350, #34177374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3519);