Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #475×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3335 |
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,d^b=de,h^b=h^78,f^c=fg,h^c=h^78,h^d=h^78776 conjugacy classes — view the full character table.
| maximal subgroup of | #34277779, #34277788, #34277814, … |
| maximal normal subgroup of | #34277779, #34277788, #34277814, … |
| maximal quotient of | #34304486, #34304506, #34305892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 16870);