Finite Group DatabasebetaFinite Group Databasebeta| order | 18130 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37×C49 · Schur multiplier (H2) = C1 |
| direct product | D5×C37×C49 |
| unambiguous semidirect product | C5⋊(C2×C37×C49) |
| Fitting, Hall | C5×C37×C49 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C37×C49 |
| Hall | C5×C49 ⋊ C2×C37 |
| Hall | C5×C37 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37×C49 | D5 |
| commutator, hypocenter | C5 | C2×C37×C49 |
| Frattini | C7 | C7×D5×C37 |
| Fitting | C5×C37×C49 | C2 |
| socle | C5×C7×C37 | C2×C7 |
| prime radical | C7×D5×C37 | C7 |
| cosocle | C5×C7 | C2×C7×C37 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C37×C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9065 |
7252 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽5)×C37×C49, C49×#10625193, C37×C49⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | AGL(1,𝔽5)×C37×C49, C49×#10625193, C37×C49⋊AGL(1,𝔽5), … |
| maximal quotient of | Dic5×C37×C49, C2×D5×C37×C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18130, 5);