Finite Group DatabasebetaFinite Group Databasebeta| order | 20988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D53×C3⋊D33 |
| unambiguous semidirect product | (C3×D53)⋊D33 |
| unambiguous semidirect product | (C11×D53)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C11×C53 ⋊ C22 |
| Hall | C11×C53 ⋊ C2×C3⋊D3 |
| Hall | C32×C53 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×C3⋊D33 |
| Sylow | C11 ⋊ C3⋊D3×D53 |
| Sylow | C32 ⋊ D11×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11×C53 | C22 |
| LCS | G ▷ C32×C11×C53 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5247 |
1428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20988, 72);