Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#135×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3269 |
478 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,d^b=de,e^b=eg,e^d=eg1177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3269×D83, C2×#24919018, #36279479, … |
| maximal normal subgroup of | #3269×D83, C2×#24919018, #36279479, … |
| maximal quotient of | #35393826, #35393946, #35394096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16065);