Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3107 |
390 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^78,f^c=fg,h^c=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34258271, #34258273, #34258304, … |
| maximal normal subgroup of | #34258271, #34258273, #34258304, … |
| maximal quotient of | #34288304, #34291206, #34291211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14579);