Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #2062 |
314 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 73 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=d,b^2=d,c^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^781118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34201123, #34201125, #34201130, … |
| maximal normal subgroup of | #34201123, #34201125, #34201130, … |
| maximal quotient of | #34192670, #34192672, #34192675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5863);