Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D3×C13×D137 |
| unambiguous semidirect product | (D3×C137)⋊(C2×C13) |
| unambiguous semidirect product | (C3×D137)⋊(C2×C13) |
| unambiguous semidirect product | D411⋊(C2×C13) |
| Fitting, socle, Hall | C3×C13×C137 ⋊ C22 |
| derived, Hall | C3×C137 ⋊ C22×C13 |
| Hall | C13×C137 ⋊ C2×D3 |
| Sylow | C137 ⋊ C2×D3×C13 |
| Hall | C3×C13 ⋊ C2×D137 |
| Sylow | C3 ⋊ C2×C13×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D3×D137 |
| commutator, cosocle, hypocenter | C3×C137 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C137 | C22 |
| LCS | G ▷ C3×C137 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5343 |
2730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 32);