Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #331×D83 |
| Fitting | #331×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#331 |
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
817 conjugacy classes — view the full character table.
| maximal subgroup of | #1402×D83, C2×#331×D83, #1540×D83, … |
| maximal normal subgroup of | #1402×D83, C2×#331×D83, #1540×D83, … |
| maximal quotient of | #1270×D83, #35292377, #35292679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3149);