Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×C22⋊D167 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 63 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 | (C22⋊D167)⋊C16, C16×C22⋊D167, #36325960, … |
| maximal normal subgroup of | (C22⋊D167)⋊C16, C16×C22⋊D167, #36325960, … |
| maximal quotient of | C8×#14581935, C8×#14581938, C8×#14581937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 613);