Finite Group DatabasebetaFinite Group Databasebeta| order | 28294 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D43⋊C7 |
| unambiguous semidirect product | D43⋊(C7×C47) |
| unambiguous semidirect product | (C43⋊C7)⋊(C2×C47) |
| unambiguous semidirect product | (C47×D43)⋊C7 |
| Fitting, socle, Hall | C43×C47 ⋊ C2×C7 |
| derived, Sylow | C43 ⋊ C2×C7×C47 |
| Hall | C47×C43⋊C7 ⋊ C2 |
| Hall | C47×D43 ⋊ C7 |
| Hall | C43⋊C7 ⋊ C2×C47 |
| Hall | D43 ⋊ C7×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C2×C7×C47 |
| Frattini | C1 | G |
| Fitting, socle | C43×C47 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2021 |
799 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28294, 11);