Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #3402 |
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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,b^2=e,c^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,c^b=cg,d^b=de,h^b=h^78,f^c=fg,h^c=h^78887 conjugacy classes — view the full character table.
| maximal subgroup of | #34201837, #34201841, #34201851, … |
| maximal normal subgroup of | #34201837, #34201841, #34201851, … |
| maximal quotient of | #34305146, #34307157, #34308087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17592);