Finite Group DatabasebetaFinite Group Databasebeta| order | 36771 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14524190⋊C17 |
| Fitting, socle, derived, Hall | C7×C103 ⋊ C3×C17 |
| Hall | C7×C103⋊C17 ⋊ C3 |
| Hall | #14524190 ⋊ C17 |
| Hall | C103⋊C17 ⋊ ΓL(1,𝔽8) |
| Sylow | C103 ⋊ C17×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C103⋊C3)⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C103 | C3×C17 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 721 |
Polycyclic presentation:
3,7,17,103|b^a=b^2,d^a=d^56,d^c=d^7299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36771, 9);