Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊AGL(1,𝔽29) |
| unambiguous semidirect product | (C7⋊#1181)⋊C7 |
| Fitting, socle, derived | C7×C29 ⋊ C4×C7 |
| Hall | C7×C29⋊C7 ⋊ C4 |
| Sylow | C29 ⋊ C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C29 | C4×C7 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,2,7,29|a^2=c,d^a=d^6,e^a=e^17,e^b=e^16,e^c=e^2877 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 29);