Finite Group DatabasebetaFinite Group Databasebeta| order | 3430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C1 |
| direct product | D5×7−1+2 |
| Fitting, Hall | C5×7−1+2 ⋊ C2 |
| Sylow | C5 ⋊ C2×7−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C7 | C72×D5 |
| commutator, socle, cosocle | C5×C7 | C2×C72 |
| Fitting | C5×7−1+2 | C2 |
| prime radical | C72×D5 | C7 |
| hypercenter | 7−1+2 | D5 |
| hypocenter | C5 | C2×7−1+2 |
| LCS | G ▷ C5×C7 ▷ C5 | |
| UCS | C1 ◁ C7 ◁ 7−1+2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 245 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D49⋊C7, D5×(C49⋊C3)⋊C7, AGL(1,𝔽5)×7−1+2, … |
| maximal normal subgroup of | D5×D49⋊C7, D5×(C49⋊C3)⋊C7, AGL(1,𝔽5)×7−1+2, … |
Past the SmallGroups library coverage — no SmallGroups id.