Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C79 ⋊ #1440 |
736 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 197 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,c^2=d,b^a=bd,c^a=ce,h^a=h^78,c^b=cf1604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175587, #34180844, #34180845, … |
| maximal normal subgroup of | #34175587, #34180844, #34180845, … |
| maximal quotient of | #34176191, #34176193, #34195838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2759);