Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #364×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2166 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,c^b=cg,e^b=eg,h^b=h^82,e^c=eg,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35315918, #35315920, #35315923, … |
| maximal normal subgroup of | #35315918, #35315920, #35315923, … |
| maximal quotient of | #35319421, #35319473, #35319744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6325);