Finite Group DatabasebetaFinite Group Databasebeta| order | 14070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#14584196 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C67 | C2×C3 |
| LCS | G ▷ C5×C7×C67 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2345 |
Polycyclic presentation:
2,3,5,7,67|c^a=c^4,e^a=e^66,d^b=d^2,e^b=e^29405 conjugacy classes — view the full character table.
| maximal subgroup of | #14584200⋊D5, #14584204⋊D5, D5×#14584196, … |
| maximal normal subgroup of | #14584200⋊D5, #14584204⋊D5, D5×#14584196, … |
| maximal quotient of | #43244864, C2×C5⋊#14584196 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14070, 40);