Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128143 |
| Fitting | C2×Q32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#510 |
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
934 conjugacy classes — view the full character table.
| maximal subgroup of | #35557730, C4×#19128143, #35557752, … |
| maximal normal subgroup of | #35557730, C4×#19128143, #35557752, … |
| maximal quotient of | C2×#24909181, C2×#24909174, C2×#24909248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17640);