Finite Group DatabasebetaFinite Group Databasebeta| order | 23310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3885 |
| unambiguous semidirect product | C5⋊(C3⋊D777) |
| unambiguous semidirect product | C7⋊(C3⋊D555) |
| unambiguous semidirect product | C37⋊(C3⋊D105) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C7×C37 | C2 |
| LCS | G ▷ C32×C5×C7×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11655 |
Polycyclic presentation:
2,3^2,5,7,37|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^365829 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23310, 168);