Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C83 ⋊ #1274 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,e^a=ef,h^a=h^82,d^b=df1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291179, #35291180, #35291217, … |
| maximal normal subgroup of | #35291179, #35291180, #35291217, … |
| maximal quotient of | C83⋊#7014, #35290936, #35290938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2339);