Finite Group Databasebeta

C7×C9×D11⋊C25 #46831377

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×D11⋊C25
unambiguous semidirect productD11⋊(C7×C9×C25)
unambiguous semidirect product(C9×D11)⋊(C7×C25)
unambiguous semidirect product(C11⋊C25)⋊(C2×C7×C9)
unambiguous semidirect product(C7×C9×D11)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C7×C9×C25
HallC7×C9×C11⋊C25 ⋊ C2
HallC9×C11⋊C25 ⋊ C2×C7
HallC7×C11⋊C25 ⋊ C2×C9
HallC7×C9×D11 ⋊ C25
HallC7×C9×C11 ⋊ C2×C25
HallC11⋊C25 ⋊ C2×C7×C9
HallC9×D11 ⋊ C7×C25
HallC7×D11 ⋊ C9×C25
HallC9×C11 ⋊ C2×C7×C25
HallC7×C11 ⋊ C2×C9×C25
HallD11 ⋊ C7×C9×C25

Subgroups

subgroupG/H
center, hypercenterC5×C7×C9AGL(1,𝔽11)
commutator, hypocenterC11C2×C7×C9×C25
FrattiniC3×C5C3×C7×AGL(1,𝔽11)
FittingC5×C7×C9×C11C2×C5
socleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×C7×D11C3×C5
cosocleC3×C5×C11C2×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C5×C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 20);