Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×(C2×D167)⋊C4 |
| Fitting | C2×C42×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323908, C8×(C2×D167)⋊C4, #36323913, … |
| maximal normal subgroup of | #36323908, C8×(C2×D167)⋊C4, #36323913, … |
| maximal quotient of | C4×C167⋊#95, (C2×D167)⋊#95, #36322362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 398);