Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14581951 |
| Fitting | C4×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×#41 |
310 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322519, #36322524, #36322571, … |
| maximal normal subgroup of | #36322519, #36322524, #36322571, … |
| maximal quotient of | C4×#19128790, C4×#19128794, C4×Q8×Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1019);