Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D7×Dic5 |
| derived | C5×C7 ⋊ C2×C4×C5 |
| Hall | C52×C7 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D7 |
| Sylow | C7 ⋊ C2×C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D5×D7 |
| commutator, hypocenter | C5×C7 | C2×C4×C5 |
| Frattini | C2 | C5×D5×D7 |
| Fitting, socle | C2×C52×C7 | C22 |
| prime radical | C2×C52×D7 | C2 |
| cosocle | C2×C5×C7 | C22×C5 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C5 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic5×AGL(1,𝔽7), C4×C5×D5×D7, D7×#6036, … |
| maximal normal subgroup of | C5×Dic5×AGL(1,𝔽7), C4×C5×D5×D7, D7×#6036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 55);