Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #413×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1914 |
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 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=df,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,e^b=eg,f^b=fg,h^b=h^78,d^c=dg,f^c=fg887 conjugacy classes — view the full character table.
| maximal subgroup of | #34204041, #34204044, #34204048, … |
| maximal normal subgroup of | #34204041, #34204044, #34204048, … |
| maximal quotient of | #34183802, #34183812, #34184250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5055);