Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic79⋊C32 |
| Sylow | C79 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^782576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C32×D79, C2×Dic79⋊C32, #34208750, … |
| maximal normal subgroup of | C4⋊C32×D79, C2×Dic79⋊C32, #34208750, … |
| maximal quotient of | #34175934, #34175941, #34175955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2705);