Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C1049 ⋊ C2 |
| Sylow | C1049 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D1049 |
| commutator, socle | C2×C1049 | C2×C4 |
| Fitting | C8×C1049 | C2 |
| prime radical | C2×D1049 | C4 |
| cosocle | C4×C1049 | C22 |
| hypercenter | C8 | D1049 |
| hypocenter | C1049 | M16 |
| LCS | G ▷ C2×C1049 ▷ C1049 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8392 |
Polycyclic presentation:
2^4,1049|a^2=c,c^2=d,b^a=bd,e^b=e^10484202 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D1049, C2×#30680899, #46776957, … |
| maximal normal subgroup of | M16×D1049, C2×#30680899, #46776957, … |
| maximal quotient of | #46776861, #46776863, #46776880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 23);