Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#13050580 |
| Sylow | C83 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35393834, #35393837, #35393842, … |
| maximal normal subgroup of | #35393834, #35393837, #35393842, … |
| maximal quotient of | #35394585, #35394591, #35394600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16258);