Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #486×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1706 |
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^78,h^c=h^78896 conjugacy classes — view the full character table.
| maximal subgroup of | #1706×D79, C2×#23762991, #34275928, … |
| maximal normal subgroup of | #1706×D79, C2×#23762991, #34275928, … |
| maximal quotient of | #34182039, #34188006, #34188008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4101);