Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #417×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3006 |
806 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^78,e^b=eg,h^c=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #34325531, #34325535, #34325564, … |
| maximal normal subgroup of | #34325531, #34325535, #34325564, … |
| maximal quotient of | #34260665, #34260704, #34260743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13763);