Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C1049 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16862310 |
| commutator, hypocenter | C1049 | C2×C8 |
| Frattini | C2 | C2×#16862310 |
| Fitting | C4×C1049 | C4 |
| socle | C2×C1049 | C2×C4 |
| prime radical | C2×D1049 | C4 |
| cosocle | Dic1049 | C22 |
| LCS | G ▷ C1049 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8392 |
Polycyclic presentation:
2^4,1049|a^2=c,c^2=d,e^a=e^623,e^b=e^1048,e^c=e^10481064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16862310, #46777005, #46777013, … |
| maximal normal subgroup of | C8×#16862310, #46777005, #46777013, … |
| maximal quotient of | C4×#22554216, #46777008, #46777018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 48);