Finite Group DatabasebetaFinite Group Databasebeta| order | 28294 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊(D43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊D47 |
| unambiguous semidirect product | D2021⋊C7 |
| Fitting, socle, derived, Hall | C43×C47 ⋊ C2×C7 |
| Hall | C47×C43⋊C7 ⋊ C2 |
| Hall | D2021 ⋊ C7 |
| Hall | C43⋊C7 ⋊ D47 |
| Sylow | C47 ⋊ D43⋊C7 |
| Sylow | C43 ⋊ C7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C47 | C2×C7 |
| LCS | G ▷ C43×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2021 |
Polycyclic presentation:
2,7,43,47|c^a=c^42,d^a=d^46,c^b=c^41316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28294, 12);