Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#135×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2186 |
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^78,d^b=df,f^b=fg1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2186×D79, C2×#23765323, #34442047, … |
| maximal normal subgroup of | #2186×D79, C2×#23765323, #34442047, … |
| maximal quotient of | #34200377, #34200721, #34201481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6433);