Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2566 |
548 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 169 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=eg,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35302071, #35302073, #35314063, … |
| maximal normal subgroup of | #35302071, #35302073, #35314063, … |
| maximal quotient of | #35326668, #35326956, #35327282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9706);