Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #489×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3376 |
346 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,d^2=eg,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 | #3376×D83, C2×#24920289, #36284214, … |
| maximal normal subgroup of | #3376×D83, C2×#24920289, #36284214, … |
| maximal quotient of | #35421074, #35421270, #35423396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17336);