Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14581949 |
| Fitting | C4×D4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322517, #36322522, #36322569, … |
| maximal normal subgroup of | #36322517, #36322522, #36322569, … |
| maximal quotient of | C4×#19128788, C4×#19128790, C4×(C22⋊D167)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1016);