Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×D167 |
| Fitting | C2×Q16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #358×D167, #36325856, #362×D167, … |
| maximal normal subgroup of | #358×D167, #36325856, #362×D167, … |
| maximal quotient of | C2×#103×D167, C2×#107×D167, C4×Q16×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1324);