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 ⋊ #1986 |
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 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=e,d^2=g,b^a=bd,c^a=ce,h^a=h^78,d^b=dg,f^b=fg1598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180155, #34180160, #34180162, … |
| maximal normal subgroup of | #34180155, #34180160, #34180162, … |
| maximal quotient of | #34188250, #34188254, #34188259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5454);