Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic1046 |
| Sylow | C523 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16736 |
4196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45689935, #45689937, C4×#22552629, … |
| maximal normal subgroup of | #45689935, #45689937, C4×#22552629, … |
| maximal quotient of | C4×C4⋊Dic523, C4×Dic523⋊C4, #45690088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 112);