Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1998 |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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=def,c^2=eg,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^78,d^b=dg,f^b=fg,h^b=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180582, #34180584, #34180589, … |
| maximal normal subgroup of | #34180582, #34180584, #34180589, … |
| maximal quotient of | #34188318, #34188323, #34188370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5504);