Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C83 ⋊ #1398 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,c^b=cg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1398×D83, C2×#24905598, #35324590, … |
| maximal normal subgroup of | #1398×D83, C2×#24905598, #35324590, … |
| maximal quotient of | #35291733, #35291738, #35292092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2645);