Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19127974 |
| Sylow | C83 ⋊ C2×#473 |
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19127974, #35411292, #35411313, … |
| maximal normal subgroup of | C4×#19127974, #35411292, #35411313, … |
| maximal quotient of | C2×#24906826, C2×#24906850, C2×#24906884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14221);