Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #460×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3224 |
408 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^82,c^b=ce,d^b=dg,h^b=h^82,f^c=fg,h^d=h^82805 conjugacy classes — view the full character table.
| maximal subgroup of | #3224×D83, C2×#24918562, #36275814, … |
| maximal normal subgroup of | #3224×D83, C2×#24918562, #36275814, … |
| maximal quotient of | #35413777, #35414181, #35415012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15609);