Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D55 |
| unambiguous semidirect product | (C5×D7)⋊(C7×D11) |
| unambiguous semidirect product | (C11×D7)⋊(C7×D5) |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C22 |
| derived | C5×C7×C11 ⋊ C22×C7 |
| Hall | C72×C11 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×D55 |
| Sylow | C11 ⋊ C7×D5×D7 |
| Sylow | C5 ⋊ C7×D7×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D55 |
| commutator, cosocle, hypocenter | C5×C7×C11 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C22 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups.
1015 conjugacy classes — view the full character table.
| maximal subgroup of | D55×#64418, C7×AGL(1,𝔽7)×D55, D7×ΓL(1,𝔽8)×D55, … |
| maximal normal subgroup of | C7×AGL(1,𝔽7)×D55, D7×ΓL(1,𝔽8)×D55, D55×#64423, … |
| maximal quotient of | C3×C7×D7×D55, C7×D7×D165, C7×D21×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 87);