Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C8×Dic83 |
| Sylow | C83 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294905, #323×Dic83, #35294909, … |
| maximal normal subgroup of | #35294905, #323×Dic83, #35294909, … |
| maximal quotient of | C22⋊C8×C83⋊C8, #35294875, #35294884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4270);