Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19128821 |
| Fitting | C22×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324523, #36324539, #36324541, … |
| maximal normal subgroup of | #36324523, #36324539, #36324541, … |
| maximal quotient of | C2×#24923134, C2×#24923159, C2×#24923170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1067);