Finite Group DatabasebetaFinite Group Databasebeta| order | 37380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽7))⋊D89 |
| unambiguous semidirect product | D445⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D89)⋊D5 |
| unambiguous semidirect product | (D35⋊D89)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C89 | C22×C3 |
| LCS | G ▷ C5×C7×C89 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3115 |
Polycyclic presentation:
2^2,3,5,7,89|e^a=e^6,f^a=f^88,d^b=d^4,e^b=e^6,e^c=e^2776 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37380, 42);