Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #442×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^82,e^b=eg,h^c=h^82,h^d=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(1,ℤ/8)×D83, C2×#24916274, C4×#19128497, … |
| maximal normal subgroup of | C4×AGL(1,ℤ/8)×D83, C2×#24916274, C4×#19128497, … |
| maximal quotient of | #35373821, #35373990, #35374006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13321);