Finite Group DatabasebetaFinite Group Databasebeta| order | 840 |
| isoclinism | isoclinic class of D7×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | D7×A5 |
| unambiguous semidirect product | C7⋊(C2×A5) |
| Fitting, Sylow | C7 ⋊ C2×A5 |
| socle, derived | C7×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C7×A5 | C2 |
| Fitting, cosocle | C7 | C2×A5 |
| LCS | G ▷ C7×A5 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 35 |
25 conjugacy classes — view the full character table.
| maximal subgroup of | D7×S5, C2×D7×A5, A5×SL(2,𝔽8), … |
| maximal normal subgroup of | D7×S5, C2×D7×A5 |
| maximal quotient of | Dic7×A5, D7×SL(2,𝔽5), C7⋊#6732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(840, 137);