Finite Group DatabasebetaFinite Group Databasebeta| order | 14070 |
| isoclinism | isoclinic class of C5⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×C5⋊AGL(1,𝔽7) |
| unambiguous semidirect product | C5⋊(AGL(1,𝔽7)×C67) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D5×C67) |
| unambiguous semidirect product | D35⋊(C3×C67) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | C5⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C5×C7 | C2×C3×C67 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C67 | C2×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C67 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2345 |
1139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14070, 42);