Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊(C83⋊C8) |
| Sylow | C83 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 87 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=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^82,d^b=df,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16⋊C8×D83, C2×SD16⋊(C83⋊C8), #35373805, … |
| maximal normal subgroup of | SD16⋊C8×D83, C2×SD16⋊(C83⋊C8), #35373805, … |
| maximal quotient of | #35295183, #35295190, #35295655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3323);