Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×Dic83 |
| Sylow | C83 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 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 | #35410273, #453×Dic83, #35410284, … |
| maximal normal subgroup of | #35410273, #453×Dic83, #35410284, … |
| maximal quotient of | #518×Dic83, #520×Dic83, #534×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17718);