Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #346×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2164 |
138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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,h^a=h^82,c^b=cg,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2164×D83, C2×#24909271, #35557487, … |
| maximal normal subgroup of | #2164×D83, C2×#24909271, #35557487, … |
| maximal quotient of | #35319410, #35319442, #35319720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6318);