Finite Group DatabasebetaFinite Group Databasebeta| order | 29370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊(D89⋊C11)) |
| unambiguous semidirect product | C5⋊(C3⋊(D89⋊C11)) |
| unambiguous semidirect product | (C89⋊C11)⋊D15 |
| unambiguous semidirect product | D1335⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C89 | C2×C11 |
| LCS | G ▷ C3×C5×C89 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1335 |
Polycyclic presentation:
2,3,5,11,89|b^a=b^2,c^a=c^4,e^a=e^88,e^d=e^64159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29370, 25);