Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic1049 |
| derived, Sylow | C1049 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D1049 |
| commutator, hypocenter | C1049 | C22×C4 |
| Frattini | C2 | C22×D1049 |
| Fitting, socle, prime radical | C23×C1049 | C2 |
| cosocle | C2×C1049 | C23 |
| LCS | G ▷ C1049 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16784 |
4208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46776858, C2×C4×Dic1049, C2×#30680893, … |
| maximal normal subgroup of | #46776858, C2×C4×Dic1049, C2×#30680893, … |
| maximal quotient of | C2×C4×Dic1049, C2×C22⋊Dic1049, C2×C4⋊Dic1049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 33);