Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#14582115 |
| unambiguous semidirect product | #13062438⋊C8 |
| Fitting | C4×C337 ⋊ C8 |
| derived, Sylow | C337 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14582115 |
| commutator, hypocenter | C337 | C4×C8 |
| Frattini | C2 | C2×#14582115 |
| Fitting | C4×C337 | C8 |
| socle | C2×C337 | C2×C8 |
| prime radical | C2×D337 | C2×C4 |
| cosocle | C2×#13062438 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14582115, #36342389, D4⋊#14582115, … |
| maximal normal subgroup of | C8×#14582115, #36342389, D4⋊#14582115, … |
| maximal quotient of | C8×#14582115, #36342389, (C2×#14582115)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 237);