Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #500×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3353 |
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^78,f^c=fg,h^c=h^78,h^d=h^78887 conjugacy classes — view the full character table.
| maximal subgroup of | #34279188, #34279190, #34279233, … |
| maximal normal subgroup of | #34279188, #34279190, #34279233, … |
| maximal quotient of | #34304691, #34304739, #34306014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17093);