Finite Group DatabasebetaFinite Group Databasebeta| order | 23310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#17987958 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C37 | C2×C9 |
| prime radical | C7×C5⋊(D37⋊C3) | C3 |
| cosocle | C5×C7×C37⋊C3 | C2×C3 |
| LCS | G ▷ C5×C7×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1295 |
Polycyclic presentation:
2,3^2,5,7,37|b^3=c,d^a=d^4,f^a=f^36,e^b=e^2,f^b=f^16,f^c=f^26130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23310, 70);