Finite Group DatabasebetaFinite Group Databasebeta| order | 21567 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C79⋊C13 |
| unambiguous semidirect product | C7⋊(C3×C79⋊C13) |
| unambiguous semidirect product | (ΓL(1,𝔽8)×C79)⋊C13 |
| Fitting, socle, derived, Hall | C7×C79 ⋊ C3×C13 |
| Hall | C7×C79⋊C13 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C79 ⋊ C13 |
| Sylow | C79 ⋊ C13×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C79 | C3×C13 |
| LCS | G ▷ C7×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 553 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21567, 17);