Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q16×Dic166 |
| Sylow | C83 ⋊ Q8×Q16 |
336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1183 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35318093, #35318097, #35318121, … |
| maximal normal subgroup of | #35318093, #35318097, #35318121, … |
| maximal quotient of | #103×Dic166, Q16×Dic83⋊C4, Q16×C4⋊Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17394);