Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #346×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2163 |
152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 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=cg,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35313445, #35313447, #35313450, … |
| maximal normal subgroup of | #35313445, #35313447, #35313450, … |
| maximal quotient of | #35319405, #35319436, #35319714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6311);