Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | #126×Dic83 |
| Sylow | C83 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#126×D83, C2×#126×Dic83, C4×#19128234, … |
| maximal normal subgroup of | C4×#126×D83, C2×#126×Dic83, C4×#19128234, … |
| maximal quotient of | #388×Dic83, #387×Dic83, #383×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7062);