Finite Group DatabasebetaFinite Group Databasebeta| order | 18130 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×D49 |
| unambiguous semidirect product | C49⋊(C2×C5×C37) |
| Fitting, Hall | C5×C37×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C5×C37 |
| Hall | C37×C49 ⋊ C2×C5 |
| Hall | C5×C49 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C5×C37 |
| Frattini | C7 | C5×D7×C37 |
| Fitting | C5×C37×C49 | C2 |
| socle | C5×C7×C37 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C5×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9065 |
4810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D37×D49, D5×C37×D49, D49×D185, … |
| maximal normal subgroup of | C5×D37×D49, D5×C37×D49, D49×D185, … |
| maximal quotient of | C5×C37×Dic49, C2×C5×C37×D49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18130, 3);