Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #479×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3080 |
384 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^78,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3080×D79, C2×#23773219, #35155811, … |
| maximal normal subgroup of | #3080×D79, C2×#23773219, #35155811, … |
| maximal quotient of | #34287768, #34289241, #34289245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14329);