Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic25 |
| derived, Sylow | C25 ⋊ C4×C7 |
| Hall | C7×C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D25 |
| commutator, hypocenter | C25 | C4×C7 |
| Frattini | C2×C5 | C7×D5 |
| Fitting | C2×C7×C25 | C2 |
| socle, prime radical | C2×C5×C7 | D5 |
| cosocle | C2×C25 | C2×C7 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C7 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 700 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#6016, C7⋊#6016, #13063718, … |
| maximal normal subgroup of | C7×#6016, C7⋊#6016, #13063718, … |
| maximal quotient of | C7×#6014, C2×C7×Dic25, C3×C7×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 1);