Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2086 |
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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=d,c^2=d,e^2=g,b^a=bd,c^a=ce,h^a=h^78,c^b=cf,h^b=h^78,e^c=eg1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2086×D79, C2×#23764892, #34317331, … |
| maximal normal subgroup of | #2086×D79, C2×#23764892, #34317331, … |
| maximal quotient of | #34193179, #34193189, #34193214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6002);