Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | #447×D83 |
| Fitting | #447×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 155 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 | #1595×D83, #1597×D83, #1598×D83, … |
| maximal normal subgroup of | #1595×D83, #1597×D83, #1598×D83, … |
| maximal quotient of | #1595×D83, #1607×D83, #1598×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13683);