Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C83⋊#1309 |
| Sylow | C83 ⋊ #1309 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|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^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291947, #35291948, #35292025, … |
| maximal normal subgroup of | #35291947, #35291948, #35292025, … |
| maximal quotient of | #35290979, #35290980, #35291000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2423);