Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D7×ΓL(1,𝔽8)⋊D37 |
| unambiguous semidirect product | (D7×ΓL(1,𝔽8))⋊D37 |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C22×C3 |
| Hall | D7×D259 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C37 ⋊ C22 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×D37 |
| Sylow | C72 ⋊ C2×C3×D37 |
| Sylow | C37 ⋊ D7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C37 | C22×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1554 |
485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 199);