Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#14581749 |
| Fitting | C43×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#117 |
752 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 357 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 | #35293841, #35293847, #35293850, … |
| maximal normal subgroup of | #35293841, #35293847, #35293850, … |
| maximal quotient of | C4×#19127547, C42×(C2×D83)⋊C4, C42×Dic83⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6852);