Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#19127888 |
| Fitting | C2×H(5,𝔽2)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1426 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35321661, #35321667, #35321675, … |
| maximal normal subgroup of | #35321661, #35321667, #35321675, … |
| maximal quotient of | C2×#24906381, C2×#24906415, C2×#24906386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13894);