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C2×C11×D41⋊C5 #22583181

order9020
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D41⋊C5
unambiguous semidirect productD41⋊(C2×C5×C11)
unambiguous semidirect product(C2×D41)⋊(C5×C11)
unambiguous semidirect product(C41⋊C5)⋊(C22×C11)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C11)

Splittings

Fitting, socleC2×C11×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C5×C11
HallC11×C41⋊C5 ⋊ C22
HallC2×C11×D41 ⋊ C5
HallC11×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C22×C11
HallC2×D41 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D41⋊C5
commutator, hypocenterC41C22×C5×C11
FrattiniC1G
Fitting, socleC2×C11×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C11×D41⋊C5, C2×C3×C11×D41⋊C5, C2×C11×C3⋊(D41⋊C5)
maximal normal subgroup ofC2×C3×C11×D41⋊C5
maximal quotient ofD3×C11×D41⋊C5, C2×C3×C11×D41⋊C5, C2×C11×C3⋊(D41⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9020, 52);