Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C79⋊#1309 |
| Sylow | C79 ⋊ #1309 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^781118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175812, #34175813, #34175890, … |
| maximal normal subgroup of | #34175812, #34175813, #34175890, … |
| maximal quotient of | #34174844, #34174845, #34174865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2423);