Finite Group DatabasebetaFinite Group Databasebeta| order | 11620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D415 |
| unambiguous semidirect product | (C5×D7)⋊D83 |
| unambiguous semidirect product | (D7×C83)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C83 ⋊ C22 |
| Hall | C7×C83 ⋊ C2×D5 |
| Hall | C5×C83 ⋊ C2×D7 |
| Sylow | C83 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D83 |
| Sylow | C7 ⋊ C2×D415 |
| Sylow | C5 ⋊ D7×D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C83 | C22 |
| LCS | G ▷ C5×C7×C83 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×D415, C3×D7×D415, D7×D1245, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D415, C3×D7×D415 |
| maximal quotient of | C3×D7×D415, D7×D1245, D21×D415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11620, 18);