Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #1924 |
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^78,c^b=cg,h^b=h^78,h^c=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1924×D79, C2×#23764016, #34290565, … |
| maximal normal subgroup of | #1924×D79, C2×#23764016, #34290565, … |
| maximal quotient of | #34186473, #34186480, #34186487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5126);