Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of Dic70 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D140 |
| unambiguous semidirect product | C4⋊(C5×D35) |
| Fitting | C4×C52×C7 ⋊ C2 |
| Hall | C52×C7 ⋊ D4 |
| Sylow | C52 ⋊ D28 |
| Sylow | C7 ⋊ C5×D20 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C2×D35 |
| commutator, cosocle | C2×C5×C7 | C22×C5 |
| Frattini | C2 | C2×C5×D35 |
| Fitting | C4×C52×C7 | C2 |
| socle | C2×C52×C7 | C22 |
| hypercenter | C4×C5 | D35 |
| hypocenter | C5×C7 | C5×D4 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 98);