Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C83 ⋊ #1726 |
328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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=d,b^2=e,c^2=f,d^2=g,c^b=cg,h^c=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291263, #35291265, #35294843, … |
| maximal normal subgroup of | #35291263, #35291265, #35294843, … |
| maximal quotient of | C8×#14581702, C8×#14581703, #35293759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4196);