Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14581738 |
| Sylow | C83 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316135, C8×#14581738, #35316147, … |
| maximal normal subgroup of | #35316135, C8×#14581738, #35316147, … |
| maximal quotient of | C8×#14581738, #35316318, #35316320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6367);