Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1419 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^78,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^781586 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1419×D79, C2×#23761591, #34208744, … |
| maximal normal subgroup of | #1419×D79, C2×#23761591, #34208744, … |
| maximal quotient of | #34175726, #34175831, #34175903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2701);