Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of C7⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C5×C7⋊#170 |
| unambiguous semidirect product | C7⋊(C5×#170) |
| derived | C5×C7 ⋊ C5×C8 |
| Hall | C52×C7 ⋊ C8 |
| Sylow | C52 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ C5×#170 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C7⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C7 | C5×C8 |
| Frattini | C2 | C5×C7⋊AGL(1,𝔽5) |
| Fitting, socle, prime radical | C2×C52×C7 | C4 |
| cosocle | C7×Dic5 | C2×C5 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 280 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 48);