Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #470×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3063 |
472 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^82,d^c=dg,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #3063×D83, C2×#24917151, #36271657, … |
| maximal normal subgroup of | #3063×D83, C2×#24917151, #36271657, … |
| maximal quotient of | #35387896, #35387918, #35387940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14198);