Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #510×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,h^b=h^78,d^c=dg,h^d=h^78656 conjugacy classes — view the full character table.
| maximal subgroup of | #34445023, #34445025, #34445034, … |
| maximal normal subgroup of | #34445023, #34445025, #34445034, … |
| maximal quotient of | #34441186, #34441187, #34441312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17662);