Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic1042 |
| Sylow | C521 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16672 |
4180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45687162, #45687164, C4×#22552352, … |
| maximal normal subgroup of | #45687162, #45687164, C4×#22552352, … |
| maximal quotient of | C4×C4⋊Dic521, C4×#22552343, #45687315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 112);