Finite Group DatabasebetaFinite Group Databasebeta| order | 14910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊(D71⋊C5)) |
| unambiguous semidirect product | C7⋊(C3⋊(D71⋊C5)) |
| unambiguous semidirect product | (C71⋊C5)⋊D21 |
| unambiguous semidirect product | D1491⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C71 | C2×C5 |
| LCS | G ▷ C3×C7×C71 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1491 |
Polycyclic presentation:
2,3,5,7,71|b^a=b^2,d^a=d^6,e^a=e^70,e^c=e^54207 conjugacy classes — view the full character table.
| maximal subgroup of | D21×D71⋊C5, D7×C3⋊(D71⋊C5), D3×C7⋊(D71⋊C5), … |
| maximal normal subgroup of | D21×D71⋊C5, D7×C3⋊(D71⋊C5), D3×C7⋊(D71⋊C5), … |
| maximal quotient of | C3⋊(C7⋊(Dic71⋊C5)), C2×C3⋊(C7⋊(D71⋊C5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14910, 35);