Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7 |
| direct product | C7⋊D7×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×C7⋊D7) |
| unambiguous semidirect product | (C7×AGL(1,𝔽11))⋊D7 |
| unambiguous semidirect product | (D11×C7⋊D7)⋊C5 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C22×C5 |
| Hall | C72×C11⋊C5 ⋊ C22 |
| Hall | D11×C7⋊D7 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11 | C22×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 57);