Finite Group DatabasebetaFinite Group Databasebeta| order | 12220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D13×D47 |
| unambiguous semidirect product | (D13×C47)⋊(C2×C5) |
| unambiguous semidirect product | (C13×D47)⋊(C2×C5) |
| unambiguous semidirect product | D611⋊(C2×C5) |
| Fitting, socle, Hall | C5×C13×C47 ⋊ C22 |
| derived, Hall | C13×C47 ⋊ C22×C5 |
| Hall | C5×C47 ⋊ C2×D13 |
| Hall | C5×C13 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ C2×C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D13×D47 |
| commutator, cosocle, hypocenter | C13×C47 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C47 | C22 |
| LCS | G ▷ C13×C47 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D13⋊C3×D47, C3×C5×D13×D47, C5×D39×D47, … |
| maximal normal subgroup of | C5×D13⋊C3×D47, C3×C5×D13×D47 |
| maximal quotient of | C3×C5×D13×D47, C5×D39×D47, C5×D13×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12220, 12);