Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4⋊C4×D167 |
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 207 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 | #324×D167, #36322466, #340×D167, … |
| maximal normal subgroup of | #324×D167, #36322466, #340×D167, … |
| maximal quotient of | C2×#95×D167, C4×C4⋊C4×D167, C2×#24923120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 998);