Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #448×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3266 |
494 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,d^b=de,e^b=eg,h^c=h^82,e^d=eg,h^d=h^82808 conjugacy classes — view the full character table.
| maximal subgroup of | #3266×D83, C2×#24918976, #36279483, … |
| maximal normal subgroup of | #3266×D83, C2×#24918976, #36279483, … |
| maximal quotient of | #35393784, #35393904, #35394039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16023);