Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#101×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2020 |
342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,f^b=fg,h^b=h^78,d^c=dg,e^c=eg,f^c=fg,h^c=h^78884 conjugacy classes — view the full character table.
| maximal subgroup of | #2020×D79, C2×#23764520, #34315473, … |
| maximal normal subgroup of | #2020×D79, C2×#23764520, #34315473, … |
| maximal quotient of | #34188880, #34188897, #34188953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5630);