Finite Group DatabasebetaFinite Group Databasebeta| order | 21996 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C47⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C47⋊(C3×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C47⋊#261)⋊C32 |
| unambiguous semidirect product | (C3×C47⋊#261)⋊C3 |
| Fitting, socle | C3×C13×C47 ⋊ C3×C4 |
| derived, Hall | C13×C47 ⋊ C32×C4 |
| Hall | C3×C13⋊C3×C47 ⋊ C4 |
| Hall | C47⋊#261 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ Dic47 |
| Sylow | C47 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C32×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C47⋊AGL(1,𝔽13) |
| commutator, hypocenter | C13×C47 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C47 | C3×C4 |
| prime radical | C3×C47×D13⋊C3 | C2 |
| cosocle | D13×C47 | C2×C32 |
| LCS | G ▷ C13×C47 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1833 |
591 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21996, 63);