Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C17⋊(D7⋊C9)) |
| unambiguous semidirect product | C17⋊(C5⋊(D7⋊C9)) |
| unambiguous semidirect product | (C7⋊C9)⋊D85 |
| unambiguous semidirect product | D595⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(C17⋊AGL(1,𝔽7)) |
| commutator, hypocenter | C5×C7×C17 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C17 | C2×C3 |
| prime radical | C3×D595 | C3 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,17,3|b^3=f,c^a=c^4,d^a=d^6,e^a=e^16,d^b=d^2651 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C5⋊(D7⋊C9), D7⋊C9×D85, D5×C17⋊(D7⋊C9), … |
| maximal normal subgroup of | D17×C5⋊(D7⋊C9), D7⋊C9×D85, D5×C17⋊(D7⋊C9), … |
| maximal quotient of | (C7⋊C9)⋊Dic85, C2×C5⋊(C17⋊(D7⋊C9)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 24);