Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D25 |
| unambiguous semidirect product | C25⋊(C22×C7) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C7) |
| Fitting | C2×C7×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C22×C7 |
| Hall | C7×C25 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D25 |
| commutator, cosocle, hypocenter | C25 | C22×C7 |
| Frattini | C5 | C2×C7×D5 |
| Fitting | C2×C7×C25 | C2 |
| socle | C2×C5×C7 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C7 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 350 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×D25, #13063721, #13063723, … |
| maximal normal subgroup of | Dic7×D25, #13063721, #13063723, … |
| maximal quotient of | C7×Dic50, C4×C7×D25, C7×D100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 9);