Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#19129160 |
| derived, Sylow | C337 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D337 |
| commutator, hypocenter | C337 | C2×C16 |
| Frattini | C8 | C2×D337 |
| Fitting | C2×C8×C337 | C2 |
| socle, prime radical | C22×C337 | C8 |
| cosocle | C8×C337 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic337, C4×#19129160, #36341080, … |
| maximal normal subgroup of | C16×Dic337, C4×#19129160, #36341080, … |
| maximal quotient of | C4×#19129160, C22⋊#19129160, C4⋊#19129160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 84);