Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #575×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3067 |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^78,f^c=fg890 conjugacy classes — view the full character table.
| maximal subgroup of | #34295204, #34295205, #34295215, … |
| maximal normal subgroup of | #34295204, #34295205, #34295215, … |
| maximal quotient of | #34270508, #34270536, #34270576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14227);