Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #358×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2139 |
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=df,f^b=fg,h^b=h^78,h^c=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #2139×D79, C2×#23765111, #34441170, … |
| maximal normal subgroup of | #2139×D79, C2×#23765111, #34441170, … |
| maximal quotient of | #34198013, #34198257, #34198309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6221);