Finite Group DatabasebetaFinite Group Databasebeta| order | 15540 |
| isoclinism | isoclinic class of C3⋊(C7⋊AGL(1,𝔽5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C3⋊(C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C37×C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C7⋊(C37×ΓL(1,𝔽16)) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊(C7⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C3×C5×C7 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C37 | C4 |
| prime radical | C3×C7×D5×C37 | C2 |
| cosocle | C3×C7×D5 | C2×C37 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3885 |
1665 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15540, 185);