Finite Group DatabasebetaFinite Group Databasebeta| order | 23310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C7⋊C9)⋊D37) |
| unambiguous semidirect product | (C7⋊C9)⋊D185 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(ΓL(1,𝔽8)⋊D37) |
| commutator, hypocenter | C5×C7×C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C37 | C2×C3 |
| prime radical | C3×D1295 | C3 |
| LCS | G ▷ C5×C7×C37 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11655 |
Polycyclic presentation:
2,3,5,7,37,3|b^3=f,c^a=c^4,d^a=d^6,e^a=e^36,d^b=d^21401 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23310, 46);