Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #344×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1814 |
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=f,b^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^82,e^c=eg,f^c=fg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #1814×D83, C2×#24907516, #35404068, … |
| maximal normal subgroup of | #1814×D83, C2×#24907516, #35404068, … |
| maximal quotient of | #35297277, #35297282, #35297287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4563);