Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#13050577 |
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #35316167, C16×#13050577, #35316174, … |
| maximal normal subgroup of | #35316167, C16×#13050577, #35316174, … |
| maximal quotient of | C8×#14581712, C8×#14581716, C8×#14581723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3310);