Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D167 |
| Fitting | C4⋊Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #332×D167, #333×D167, #36322808, … |
| maximal normal subgroup of | #332×D167, #333×D167, #36322808, … |
| maximal quotient of | #384×D167, #389×D167, #391×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1090);