Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of D5×C3⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D5×C3⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C3×D5)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (D5×ΓL(1,𝔽8))⋊D3 |
| unambiguous semidirect product | (D5×D21)⋊C3 |
| Fitting, socle, derived | C3×C5×C7 ⋊ C22×C3 |
| Hall | C3×C5×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D5 |
| Hall | C5×C7 ⋊ C2×C3×D3 |
| Sylow | C7 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ C2×C3⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7 | C22×C3 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 105 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 71);