Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #495×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3280 |
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^78,h^c=h^78,e^d=eg,h^d=h^78893 conjugacy classes — view the full character table.
| maximal subgroup of | #34444726, #34444733, #34444752, … |
| maximal normal subgroup of | #34444726, #34444733, #34444752, … |
| maximal quotient of | #34277855, #34277870, #34277885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 16194);