Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#14581731 |
| Fitting | C4×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 117 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 | C8×#14581731, #35313382, #35313384, … |
| maximal normal subgroup of | C8×#14581731, #35313382, #35313384, … |
| maximal quotient of | C8×#14581731, #35313396, #35313425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6101);