Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2857 |
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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=e,c^2=f,b^a=be,c^a=cf,d^a=dg,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35303380, #35303398, #35303524, … |
| maximal normal subgroup of | #35303380, #35303398, #35303524, … |
| maximal quotient of | #35335590, #35335644, #35335659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12858);