Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C42×Dic166 |
| Sylow | C83 ⋊ C42×Q8 |
684 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 381 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 | C4×#19127433, C4×#19127431, #35295012, … |
| maximal normal subgroup of | C4×#19127433, C4×#19127431, #35295012, … |
| maximal quotient of | C42×C4⋊Dic83, C42×Dic83⋊C4, C4×#19127588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6860);