Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#106×D83 |
| Fitting | C2×#106×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#106 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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 | #1383×D83, #1386×D83, #35320959, … |
| maximal normal subgroup of | #1383×D83, #1386×D83, #35320959, … |
| maximal quotient of | C2×#334×D83, #1566×D83, C2×#24906217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13080);