Finite Group DatabasebetaFinite Group Databasebeta| order | 20972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic749 |
| unambiguous semidirect product | C7⋊(C7×Dic107) |
| unambiguous semidirect product | C107⋊(C7×Dic7) |
| derived | C7×C107 ⋊ C4×C7 |
| Hall | C72×C107 ⋊ C4 |
| Sylow | C107 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D749 |
| commutator, hypocenter | C7×C107 | C4×C7 |
| Frattini | C2 | C7×D749 |
| Fitting, socle, prime radical | C2×C72×C107 | C2 |
| cosocle | C2×C7×C107 | C2×C7 |
| LCS | G ▷ C7×C107 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2996 |
5264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20972, 13);