Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C7×C5⋊D5 |
| unambiguous semidirect product | (C2×C5)⋊(C7×D5) |
| Fitting, socle | C2×C52×C7 ⋊ C2 |
| derived, Sylow | C52 ⋊ C22×C7 |
| Hall | C52×C7 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C7 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 350 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×C5⋊D5, #13063776, #13063778, … |
| maximal normal subgroup of | Dic7×C5⋊D5, #13063776, #13063778, … |
| maximal quotient of | C7×#6045, C4×C7×C5⋊D5, C7×C4⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 34);