Finite Group DatabasebetaFinite Group Databasebeta| order | 11620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D415 |
| unambiguous semidirect product | (C2×C5)⋊(C7×D83) |
| unambiguous semidirect product | (C2×C83)⋊(C7×D5) |
| Fitting, socle | C2×C5×C7×C83 ⋊ C2 |
| derived, Hall | C5×C83 ⋊ C22×C7 |
| Hall | C5×C7×C83 ⋊ C22 |
| Hall | C7×C83 ⋊ C2×D5 |
| Sylow | C83 ⋊ C2×C7×D5 |
| Hall | C5×C7 ⋊ C2×D83 |
| Sylow | C5 ⋊ C2×C7×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D415 |
| commutator, cosocle, hypocenter | C5×C83 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C83 | C2 |
| LCS | G ▷ C5×C83 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
2926 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)×D415, D3×C7×D415, C2×C3×C7×D415, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D415, C2×C3×C7×D415 |
| maximal quotient of | D3×C7×D415, C2×C3×C7×D415, C2×C7×D1245 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11620, 23);