Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C8×#13050573 |
| Fitting | C82×C83 ⋊ C2 |
| Sylow | C83 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#13050573, #35313417, #35313420, … |
| maximal normal subgroup of | C16×#13050573, #35313417, #35313420, … |
| maximal quotient of | C8×#14581702, #35293784, #35294828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2787);