Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#14581778 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#124 |
1880 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 605 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295753, #35297015, #35297040, … |
| maximal normal subgroup of | #35295753, #35297015, #35297040, … |
| maximal quotient of | C22×#19127565, C22×#19127589, C22×#19127590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17756);