Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | #131×Dic83 |
| Sylow | C83 ⋊ C4×#131 |
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×Dic83, #35319459, #35320339, … |
| maximal normal subgroup of | #350×Dic83, #35319459, #35320339, … |
| maximal quotient of | #131×C83⋊C8, C8×#14581799, #35370014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12931);