Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #535×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3019 |
762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,h^b=h^78,e^c=eg887 conjugacy classes — view the full character table.
| maximal subgroup of | #34319556, #34319560, #34319567, … |
| maximal normal subgroup of | #34319556, #34319560, #34319567, … |
| maximal quotient of | #34260638, #34260645, #34260677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13866);