Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of D13×AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D13×AGL(1,𝔽8) |
| unambiguous semidirect product | C13⋊(C2×AGL(1,𝔽8)) |
| unambiguous semidirect product | (C23×D13)⋊C7 |
| unambiguous semidirect product | (C13×AGL(1,𝔽8))⋊C2 |
| Fitting, socle, derived | C23×C13 ⋊ C2×C7 |
| Hall | C23×D13 ⋊ C7 |
| Sylow | C13 ⋊ C2×AGL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C13 | C2×C7 |
| LCS | G ▷ C23×C13 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 170);