Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 59 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=e,c^2=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^78,d^b=dfg,e^b=eg,f^b=fg,d^c=dg,h^c=h^78647 conjugacy classes — view the full character table.
| maximal subgroup of | #2180×D79, C2×#23765292, #34441714, … |
| maximal normal subgroup of | #2180×D79, C2×#23765292, #34441714, … |
| maximal quotient of | #34200143, #34200149, #34200221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6402);