Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C83 ⋊ #1369 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^82,d^b=dg1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291875, #35291876, #35291878, … |
| maximal normal subgroup of | #35291875, #35291876, #35291878, … |
| maximal quotient of | #35291142, #35291290, C2×#24905531 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2578);