Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #501×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3349 |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^c=h^82,h^d=h^82685 conjugacy classes — view the full character table.
| maximal subgroup of | #3349×D83, C2×#24919992, #36283059, … |
| maximal normal subgroup of | #3349×D83, C2×#24919992, #36283059, … |
| maximal quotient of | #35420736, #35420766, #35422091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17039);