Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #3386 |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,c^b=cg,d^b=de,f^c=fg,h^d=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #3386×D83, C2×#24920385, #36284961, … |
| maximal normal subgroup of | #3386×D83, C2×#24920385, #36284961, … |
| maximal quotient of | #35421041, #35421052, #35422687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17432);