Finite Group DatabasebetaFinite Group Databasebeta| order | 14910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊AGL(1,𝔽71) |
| unambiguous semidirect product | (C3⋊(D71⋊C5))⋊C7 |
| unambiguous semidirect product | ((C71⋊C5)⋊C7)⋊D3 |
| unambiguous semidirect product | (C3⋊(D71⋊C7))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C71 | C2×C5×C7 |
| LCS | G ▷ C3×C71 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 213 |
Polycyclic presentation:
2,3,5,7,71|b^a=b^2,e^a=e^70,e^c=e^54,e^d=e^45108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽71), C2×C3⋊AGL(1,𝔽71) |
| maximal normal subgroup of | D3×AGL(1,𝔽71), C2×C3⋊AGL(1,𝔽71) |
| maximal quotient of | C3⋊((Dic71⋊C5)⋊C7), C2×C3⋊AGL(1,𝔽71) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14910, 38);