Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×Dic83 |
| Sylow | C83 ⋊ C4×C4⋊Q8 |
588 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 289 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #333×Dic83, #332×Dic83, #35295363, … |
| maximal normal subgroup of | #333×Dic83, #332×Dic83, #35295363, … |
| maximal quotient of | #389×Dic83, #391×Dic83, #384×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7083);