Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1585 |
168 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 61 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=cfg,d^a=df,h^a=h^82,d^b=df,h^b=h^82,h^c=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1585×D83, C2×#24906323, #35373975, … |
| maximal normal subgroup of | #1585×D83, C2×#24906323, #35373975, … |
| maximal quotient of | #35295209, #35295276, #35295676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3370);