Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #340×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2054 |
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 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|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^78,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^78,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34200711, #34200716, #34200722, … |
| maximal normal subgroup of | #34200711, #34200716, #34200722, … |
| maximal quotient of | #34192062, #34192069, #34192146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5822);