Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #564×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1658 |
182 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=g,c^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^78,d^b=df,e^b=eg,d^c=dg,e^c=efg761 conjugacy classes — view the full character table.
| maximal subgroup of | #1658×D79, C2×#23762702, #34269467, … |
| maximal normal subgroup of | #1658×D79, C2×#23762702, #34269467, … |
| maximal quotient of | #34176996, #34177023, #34177556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3812);