Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #367×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2217 |
164 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 51 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=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^78,h^c=h^78896 conjugacy classes — view the full character table.
| maximal subgroup of | #2217×D79, C2×#23765497, #34442706, … |
| maximal normal subgroup of | #2217×D79, C2×#23765497, #34442706, … |
| maximal quotient of | #34202486, #34202537, #34202605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6607);