Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C2 |
| direct product | C4×D7×C25 |
| Fitting | C4×C7×C25 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C4×C25 |
| Hall | C7×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C25 | D7 |
| commutator, hypocenter | C7 | C2×C4×C25 |
| Frattini | C2×C5 | C2×C5×D7 |
| Fitting | C4×C7×C25 | C2 |
| socle, cosocle | C2×C5×C7 | C22×C5 |
| prime radical | C2×C5×D7 | C2×C5 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C4×C25 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 700 |
500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C25×AGL(1,𝔽7) |
| maximal normal subgroup of | C4×C25×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 15);