Finite Group DatabasebetaFinite Group Databasebeta| order | 18870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×D85 |
| unambiguous semidirect product | C5⋊(D17×C37⋊C3) |
| unambiguous semidirect product | C17⋊(D5×C37⋊C3) |
| unambiguous semidirect product | (C37×D85)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C37 | C2×C3 |
| LCS | G ▷ C5×C17×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3145 |
660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27160372⋊C3, C37⋊C3×#66775, #27160376⋊C3, … |
| maximal normal subgroup of | #27160372⋊C3, C37⋊C3×#66775, #27160376⋊C3, … |
| maximal quotient of | C37⋊C3×Dic85, C2×C37⋊C3×D85 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18870, 23);