Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #450×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3114 |
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,d^c=dg,f^c=fg,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #34260852, #34260854, #34260872, … |
| maximal normal subgroup of | #34260852, #34260854, #34260872, … |
| maximal quotient of | #34288315, #34291286, #34291305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14649);