Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2991 |
394 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 221 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=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^82,c^b=ceg1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298681, #35298685, #35298695, … |
| maximal normal subgroup of | #35298681, #35298685, #35298695, … |
| maximal quotient of | #35403246, #35403431, #35403468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13642);