Finite Group Databasebeta

← Prev (#14520484) Next (#14520486) →

C2×C32×D5×C11 #14520485

order1980
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D5×C11
unambiguous semidirect productC5⋊(C22×C32×C11)
unambiguous semidirect product(C2×C5)⋊(C2×C32×C11)

Splittings

Fitting, socleC2×C32×C5×C11 ⋊ C2
derived, SylowC5 ⋊ C22×C32×C11
HallC32×C5×C11 ⋊ C22
HallC5×C11 ⋊ C22×C32
HallC32×C5 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11D5
commutator, cosocle, hypocenterC5C22×C32×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11C2
LCSG ▷ C5
UCSC1 ◁ C2×C32×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 990

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D5×C11×AGL(1,𝔽7), C2×C3×C11×C5⋊AGL(1,𝔽7), C2×C3×D5×C11×ΓL(1,𝔽8), …
maximal normal subgroup ofC2×C32×C7×D5×C11, C2×C32×D5×C121, C2×C32×D5×C112, …
maximal quotient ofC3×D5×C11×AGL(1,𝔽7), C2×C3×C11×C5⋊AGL(1,𝔽7), C2×C3×D5×C11×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 110);