Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C7⋊(C7⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C2×C7)⋊(C7⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C2×C11⋊C5)⋊(C7⋊D7) |
| unambiguous semidirect product | (C2×C7⋊D77)⋊C5 |
| Fitting, socle | C2×C72×C11 ⋊ C2×C5 |
| derived, Hall | C72×C11 ⋊ C22×C5 |
| Hall | C72×C11⋊C5 ⋊ C22 |
| Hall | C2×C7⋊D77 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊(C7⋊AGL(1,𝔽11)) |
| commutator, cosocle, hypocenter | C72×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C11 | C2×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
200 conjugacy classes of subgroups.
358 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 66);