Finite Group DatabasebetaFinite Group Databasebeta| order | 18870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×D51 |
| unambiguous semidirect product | C3⋊(C5×D17×C37) |
| unambiguous semidirect product | C17⋊(C5×D3×C37) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C17×C37 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C5×C37 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9435 |
4995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D37×D51, C5×D3×D17×C37, C5×D51⋊D37, … |
| maximal normal subgroup of | C5×D37×D51, C5×D3×D17×C37, C5×D51⋊D37, … |
| maximal quotient of | C5×C37×Dic51, C2×C5×C37×D51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18870, 12);