Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | H(3,ℤ/4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1812 |
260 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 260 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,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^b=h^82,f^c=fg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35315391, #35315393, #35315396, … |
| maximal normal subgroup of | #35315391, #35315393, #35315396, … |
| maximal quotient of | #35297264, #35297268, #35297272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4555);