Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#19127872 |
| Fitting | C2×AGL(1,ℤ/8)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
934 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19127872, #35410303, #35410340, … |
| maximal normal subgroup of | C4×#19127872, #35410303, #35410340, … |
| maximal quotient of | C2×#24906389, C2×#24906391, C2×#24906491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13844);