Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×SD16×D83 |
| Fitting | C22×SD16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1877×D83, #1880×D83, #35405831, … |
| maximal normal subgroup of | #1877×D83, #1880×D83, #35405831, … |
| maximal quotient of | C22×#102×D83, C22×#103×D83, C22×#106×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19227);