Finite Group DatabasebetaFinite Group Databasebeta| order | 20727 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C47 · Schur multiplier (H2) = C3 |
| direct product | C3×C47×#3861 |
| Fitting, socle | C3×C72×C47 ⋊ C3 |
| derived, Sylow | C72 ⋊ C32×C47 |
| Hall | C72×C47 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C47 | #3861 |
| commutator, cosocle, hypocenter | C72 | C32×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C47 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C47 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6909 |
2679 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20727, 12);