Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of C5⋊D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5⋊D35 |
| unambiguous semidirect product | (C2×C5)⋊D35 |
| unambiguous semidirect product | (C2×C7)⋊(C5⋊D5) |
| Fitting, socle | C2×C52×C7 ⋊ C2 |
| derived, Hall | C52×C7 ⋊ C22 |
| Sylow | C52 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊D35 |
| commutator, cosocle, hypocenter | C52×C7 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 350 |
178 conjugacy classes — view the full character table.
| maximal subgroup of | #13063775, #13063777, #13063778, … |
| maximal normal subgroup of | #13063775, #13063777, #13063778, … |
| maximal quotient of | #13063817, C4×C5⋊D35, C4⋊(C5⋊D35), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 35);