Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #461×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3260 |
346 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^78,f^c=fg767 conjugacy classes — view the full character table.
| maximal subgroup of | #3260×D79, C2×#23774843, #35161251, … |
| maximal normal subgroup of | #3260×D79, C2×#23774843, #35161251, … |
| maximal quotient of | #34298259, #34298264, #34298684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15953);