Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #101×D167 |
| Fitting | #101×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
935 conjugacy classes — view the full character table.
| maximal subgroup of | #355×D167, #356×D167, #36325824, … |
| maximal normal subgroup of | #355×D167, #356×D167, #36325824, … |
| maximal quotient of | #324×D167, #36322460, #36322466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 527);