Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1049 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #16862310 |
| commutator, hypocenter | C1049 | C16 |
| Fitting | C4×C1049 | C4 |
| socle, prime radical | C2×C1049 | C8 |
| cosocle | #22554209 | C2 |
| LCS | G ▷ C1049 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16784 |
Polycyclic presentation:
2^4,1049|a^2=b,b^2=c,c^2=d,e^a=e^623,e^b=e^10481064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#30680919, #46777024, #46777025, … |
| maximal normal subgroup of | C2×#30680919, #46777024, #46777025, … |
| maximal quotient of | #46777001, C2×#30680919 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 43);