Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C337 ⋊ C2 |
| Sylow | C337 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D337 |
| commutator, socle, cosocle | C22×C337 | C23 |
| Fitting | C42×C337 | C2 |
| prime radical | C22×D337 | C22 |
| hypercenter | C42 | D337 |
| hypocenter | C337 | #126 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ C42 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^3362702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D337, C2×#24924953, #36341838, … |
| maximal normal subgroup of | #126×D337, C2×#24924953, #36341838, … |
| maximal quotient of | #36341173, #36341189, #36341196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 140);