Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#19129199 |
| Fitting, socle | C2×C337 ⋊ C16 |
| derived, Sylow | C337 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19129199 |
| commutator, hypocenter | C337 | C2×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C337 | C16 |
| prime radical | C2×D337 | C8 |
| cosocle | #14582115 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
74 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19129199, C22⋊#19129199, C4⋊#19129199, … |
| maximal normal subgroup of | C4×#19129199, C22⋊#19129199, C4⋊#19129199, … |
| maximal quotient of | C4×#19129199, C22⋊#19129199, C4⋊#19129199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 246);