Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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,b^2=f,c^2=e,e^2=g,b^a=bd,h^a=h^82,h^b=h^82,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294944, #35294948, #35294956, … |
| maximal normal subgroup of | #35294944, #35294948, #35294956, … |
| maximal quotient of | C22⋊C8×C83⋊C8, #35294880, #35294897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4284);