Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#19127664 |
| Fitting | C22×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#407 |
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309634, (C2×D83)⋊#338, #35309644, … |
| maximal normal subgroup of | #35309634, (C2×D83)⋊#338, #35309644, … |
| maximal quotient of | C2×#24905789, C2×#24905792, C2×#24905795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12945);