Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#19127423 |
| Sylow | C83 ⋊ C2×#322 |
248 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291252, #35291254, #35291378, … |
| maximal normal subgroup of | #35291252, #35291254, #35291378, … |
| maximal quotient of | C4×#19127423, C2×C83⋊#1273, #35294827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2786);