Finite Group DatabasebetaFinite Group Databasebeta| order | 20972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic107 |
| unambiguous semidirect product | C107⋊(C4×C49) |
| derived, Sylow | C107 ⋊ C4×C49 |
| Hall | C49×C107 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D107 |
| commutator, hypocenter | C107 | C4×C49 |
| Frattini | C2×C7 | C7×D107 |
| Fitting | C2×C49×C107 | C2 |
| socle, prime radical, cosocle | C2×C7×C107 | C2×C7 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C2×C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20972 |
5390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20972, 3);