Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D523 |
| Fitting | Q16×C523 ⋊ C2 |
| Sylow | C523 ⋊ C2×Q16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
1841 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D523, Q32×D523, #45690644, … |
| maximal normal subgroup of | SD32×D523, Q32×D523, #45690644, … |
| maximal quotient of | #103×D523, #107×D523, #45690297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 162);