Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1397 |
68 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=bg,h^b=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292210, #1397×D83, C2×#24905596, … |
| maximal normal subgroup of | #35292210, #1397×D83, C2×#24905596, … |
| maximal quotient of | #35291731, #35291736, #35292090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2643);