Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#106×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3060 |
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=e,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^78,d^c=dg,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34205727, #34205732, #34207051, … |
| maximal normal subgroup of | #34205727, #34205732, #34207051, … |
| maximal quotient of | #34271355, #34271394, #34271447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14173);