Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#126×D83 |
| Fitting | C2×#126×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#126 |
1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 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 | #1473×D83, #35370497, C4×#126×D83, … |
| maximal normal subgroup of | #1473×D83, #35370497, C4×#126×D83, … |
| maximal quotient of | C2×#383×D83, C2×#387×D83, C2×#388×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17764);