Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #359×D83 |
| Fitting | #359×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
946 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#359×D83, #2143×D83, #35557334, … |
| maximal normal subgroup of | C2×#359×D83, #2143×D83, #35557334, … |
| maximal quotient of | #1331×D83, #1332×D83, #35314141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6232);