Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#19127682 |
| Fitting | C2×#100×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#413 |
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #35319345, #35319353, #35321885, … |
| maximal normal subgroup of | #35319345, #35319353, #35321885, … |
| maximal quotient of | C2×#24905774, C2×#24905778, #35370214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12982);