Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×Dic83 |
| Sylow | C83 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410295, #454×Dic83, #35410306, … |
| maximal normal subgroup of | #35410295, #454×Dic83, #35410306, … |
| maximal quotient of | #520×Dic83, #519×Dic83, #536×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17723);