Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D83)⋊C16 |
| Fitting | C22×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291742, #35319430, C4×(C2×D83)⋊C16, … |
| maximal normal subgroup of | #35291742, #35319430, C4×(C2×D83)⋊C16, … |
| maximal quotient of | C2×#24905386, C2×#24905402, #35313600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6117);