Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #1362 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=g,c^2=fg,d^2=efg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^78,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^781589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1362×D79, C2×#23761450, #34199511, … |
| maximal normal subgroup of | #1362×D79, C2×#23761450, #34199511, … |
| maximal quotient of | #34174998, #34175003, #34175004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2560);