Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of D7×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | Dic7×C5⋊D5 |
| derived, Hall | C52×C7 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×Dic7 |
| Sylow | C7 ⋊ C4×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×C5⋊D5 |
| commutator, hypocenter | C52×C7 | C2×C4 |
| Fitting, socle, cosocle | C2×C52×C7 | C22 |
| prime radical | C2×C7×C5⋊D5 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 700 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 63);