Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #463×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3247 |
398 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^78,f^c=fg,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3247×D79, C2×#23774723, #35161096, … |
| maximal normal subgroup of | #3247×D79, C2×#23774723, #35161096, … |
| maximal quotient of | #34298171, #34298178, #34298655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15833);