Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#19127486 |
| Fitting | C2×M32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #35319451, C4×#19127486, #35319456, … |
| maximal normal subgroup of | #35319451, C4×#19127486, #35319456, … |
| maximal quotient of | C2×#24905388, #35313480, C2×#24905404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6135);