Finite Group DatabasebetaFinite Group Databasebeta| order | 23478 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C43⋊C3)⋊C7)⋊D13 |
| unambiguous semidirect product | ((C43⋊C3)⋊D13)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C43 | C2×C3×C7 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 559 |
Polycyclic presentation:
2,3,7,13,43|d^a=d^12,e^a=e^42,e^b=e^36,e^c=e^41181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23478, 141);