Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#22554218 |
| Fitting, socle | C2×C1049 ⋊ C8 |
| derived, Sylow | C1049 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22554218 |
| commutator, hypocenter | C1049 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1049 | C8 |
| prime radical | C2×D1049 | C4 |
| cosocle | #16862310 | C22 |
| LCS | G ▷ C1049 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2098 |
278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22554218, C22⋊#22554218, C4⋊#22554218, … |
| maximal normal subgroup of | C4×#22554218, C22⋊#22554218, C4⋊#22554218, … |
| maximal quotient of | C4×#22554218, C22⋊#22554218, C4⋊#22554218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 53);