Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #548×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3271 |
488 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^78,d^b=de,e^b=eg,e^d=eg,h^d=h^781004 conjugacy classes — view the full character table.
| maximal subgroup of | #3271×D79, C2×#23774986, #35163345, … |
| maximal normal subgroup of | #3271×D79, C2×#23774986, #35163345, … |
| maximal quotient of | #34277722, #34277842, #34278067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 16096);