Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | C22×C83⋊#95 |
| Sylow | C83 ⋊ C22×#95 |
1880 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 981 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 | #35292323, #35292324, #35292325, … |
| maximal normal subgroup of | #35292323, #35292324, #35292325, … |
| maximal quotient of | C2×C4×C83⋊#95, C2×#24905685, C2×#24905686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6834);