Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #440×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3182 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^82,d^c=dg934 conjugacy classes — view the full character table.
| maximal subgroup of | #3182×D83, C2×#24918178, #36274380, … |
| maximal normal subgroup of | #3182×D83, C2×#24918178, #36274380, … |
| maximal quotient of | #35404999, #35408739, #35408741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15225);