Finite Group DatabasebetaFinite Group Databasebeta| order | 20988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×(C3⋊D3)⋊D53 |
| unambiguous semidirect product | (C3⋊D3)⋊(C11×D53) |
| unambiguous semidirect product | D159⋊(D3×C11) |
| Fitting, socle, Hall | C32×C11×C53 ⋊ C22 |
| derived, Hall | C32×C53 ⋊ C22×C11 |
| Hall | C11×C53 ⋊ D32 |
| Hall | C32×C11 ⋊ C2×D53 |
| Sylow | C53 ⋊ D32×C11 |
| Sylow | C32 ⋊ C2×C11×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | (C3⋊D3)⋊D53 |
| commutator, cosocle, hypocenter | C32×C53 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C53 | C22 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 ◁ C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3498 |
1815 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20988, 61);