Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #107×D167 |
| Fitting | #107×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#107 |
130 conjugacy classes of subgroups.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D167, #358×D167, #36325847, … |
| maximal normal subgroup of | #357×D167, #358×D167, #36325847, … |
| maximal quotient of | #335×D167, #36322895, #36322911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 581);