Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #322×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1594 |
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^82,c^b=cg,d^b=df,h^b=h^821672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316362, #35316364, #35316376, … |
| maximal normal subgroup of | #35316362, #35316364, #35316376, … |
| maximal quotient of | #35295238, #35295663, #35298360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3425);