Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #3237 |
322 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^82,f^c=fg805 conjugacy classes — view the full character table.
| maximal subgroup of | #3237×D83, C2×#24918674, #36276575, … |
| maximal normal subgroup of | #3237×D83, C2×#24918674, #36276575, … |
| maximal quotient of | #35413924, #35414161, #35414971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15721);