Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | #491×D83 |
| Fitting | #491×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#491 |
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
688 conjugacy classes — view the full character table.
| maximal subgroup of | #1356×D83, #1413×D83, #1662×D83, … |
| maximal normal subgroup of | #1356×D83, #1413×D83, #1662×D83, … |
| maximal quotient of | #1836×D83, #1935×D83, #1960×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14847);