Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 165 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=f,c^2=de,e^2=g,b^a=bd,h^a=h^78,h^b=h^78,h^c=h^781640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179030, #34179036, #34179037, … |
| maximal normal subgroup of | #34179030, #34179036, #34179037, … |
| maximal quotient of | C4⋊C8×C79⋊C8, #34179401, #34179418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4375);