Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #338×D83 |
| Fitting | #338×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#338 |
372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #1341×D83, #1342×D83, #35314564, … |
| maximal normal subgroup of | #1341×D83, #1342×D83, #35314564, … |
| maximal quotient of | #1275×D83, #35293821, #35293824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4212);