Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#19127424 |
| Fitting | C2×C22⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#323 |
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294905, C4×#19127424, #35294913, … |
| maximal normal subgroup of | #35294905, C4×#19127424, #35294913, … |
| maximal quotient of | C2×#24905283, C2×#24905288, #35292354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2816);