Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C337 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #13062438 |
| commutator, hypocenter | C337 | C2×C16 |
| Frattini | C4 | C2×#13062438 |
| Fitting | C8×C337 | C4 |
| socle | C2×C337 | C2×C8 |
| prime radical | C2×D337 | C8 |
| cosocle | #14582106 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=c,c^2=d,d^2=e,f^a=f^148,f^b=f^336,f^c=f^336704 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#13062438, #36342192, #36342217, … |
| maximal normal subgroup of | C16×#13062438, #36342192, #36342217, … |
| maximal quotient of | #36342191, #36342200, #36342226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 219);