Finite Group DatabasebetaFinite Group Databasebeta| order | 21996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C3⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C3⋊(C47×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C3⋊#261)⋊(C3×C47) |
| unambiguous semidirect product | (C47×C3⋊#261)⋊C3 |
| Fitting, socle | C3×C13×C47 ⋊ C3×C4 |
| derived | C3×C13 ⋊ C3×C4×C47 |
| Hall | C3×C13⋊C3×C47 ⋊ C4 |
| Hall | C13×C47 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ C4×C47 |
| Sylow | C13 ⋊ C3×Dic3×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C3⋊AGL(1,𝔽13) |
| commutator, hypocenter | C3×C13 | C3×C4×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C47 | C3×C4 |
| prime radical | C3×C47×D13⋊C3 | C2 |
| cosocle | C3×D13 | C2×C3×C47 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C47 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1833 |
987 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21996, 65);