Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#14581784 |
| Sylow | C83 ⋊ C4×#125 |
484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292375, #35292449, #35292452, … |
| maximal normal subgroup of | #35292375, #35292449, #35292452, … |
| maximal quotient of | C4×#19127585, C4×#19127599, C4×#19127567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7070);