Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊(C83⋊C8) |
| Sylow | C83 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24905305, C2×#24905306, #35293997, … |
| maximal normal subgroup of | C2×#24905305, C2×#24905306, #35293997, … |
| maximal quotient of | C22×#19127425, C22×#19127427, C2×#24905777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12942);