Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#19127524 |
| Sylow | C83 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19127524, #365×Dic83, #35319824, … |
| maximal normal subgroup of | C4×#19127524, #365×Dic83, #35319824, … |
| maximal quotient of | C2×#24905529, #35315962, #35316036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6279);