Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×(C2×D83)⋊C4 |
| Fitting | C24×C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C23×C22⋊C4 |
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 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 | #35292325, #35295730, C2×(C2×D83)⋊#95, … |
| maximal normal subgroup of | #35292325, #35295730, C2×(C2×D83)⋊#95, … |
| maximal quotient of | C23×C83⋊#95, C22×C4×(C2×D83)⋊C4, C22×#19127556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17667);