Finite Group Databasebeta

← Prev (#46831455) Next (#46831457) →

C5×C11⋊C5×D7⋊C9 #46831456

order34650
automorphism?
homologyAbelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×D7⋊C9
unambiguous semidirect productD7⋊(C5×C9×C11⋊C5)
unambiguous semidirect product(C7⋊C9)⋊(C2×C5×C11⋊C5)
unambiguous semidirect product(C5×D7)⋊(C9×C11⋊C5)
unambiguous semidirect product(D7×C11⋊C5)⋊(C5×C9)
unambiguous semidirect product(C11×D7⋊C9)⋊C52
unambiguous semidirect product(C5×D7×C11⋊C5)⋊C9
unambiguous semidirect product(C5×C11×D7⋊C9)⋊C5

Splittings

derived, HallC7×C11 ⋊ C2×C52×C9
HallC5×C11⋊C5×C7⋊C9 ⋊ C2
HallC5×D7×C11⋊C5 ⋊ C9
HallC5×C7×C11⋊C5 ⋊ C2×C9
HallC11×D7⋊C9 ⋊ C52
HallC11×C7⋊C9 ⋊ C2×C52
HallC11×D7 ⋊ C52×C9
HallC7⋊C9 ⋊ C2×C5×C11⋊C5
HallD7 ⋊ C5×C9×C11⋊C5
SylowC11 ⋊ C52×D7⋊C9
SylowC7 ⋊ C2×C5×C9×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C5AGL(1,𝔽7)×C11⋊C5
commutator, hypocenterC7×C11C2×C52×C9
FrattiniC3C5×AGL(1,𝔽7)×C11⋊C5
Fitting, socleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×D7×C11⋊C5C3
cosocleC3×C7×C11C2×C3×C52
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 99);