Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×Dic167 |
| Sylow | C167 ⋊ C4×#41 |
310 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×Dic167, #36323950, #36324156, … |
| maximal normal subgroup of | #104×Dic167, #36323950, #36324156, … |
| maximal quotient of | #117×Dic167, C4×D4×Dic167, C4×Q8×Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1020);