Finite Group DatabasebetaFinite Group Databasebeta| order | 23430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21462842 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C71 | C2×C5 |
| LCS | G ▷ C3×C11×C71 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2343 |
Polycyclic presentation:
2,3,5,11,71|b^a=b^2,d^a=d^10,d^c=d^4,e^c=e^5270 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23430, 56);