Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D155 |
| unambiguous semidirect product | C5⋊(C19⋊C3×D31) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C31 | C2×C3 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2945 |
711 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19⋊C3×D155, (C5⋊(D19⋊C3))⋊D31, D5×C19⋊C3×D31, … |
| maximal normal subgroup of | D19⋊C3×D155, (C5⋊(D19⋊C3))⋊D31, D5×C19⋊C3×D31, … |
| maximal quotient of | C19⋊C3×Dic155, C2×C19⋊C3×D155 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 50);