Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#19127612 |
| Fitting | C23×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#393 |
1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299390, #35299405, #35304611, … |
| maximal normal subgroup of | #35299390, #35299405, #35304611, … |
| maximal quotient of | C2×#24905705, C2×#24905722, C2×#24905734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7709);