Finite Group Databasebeta

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C4×C53×C11⋊C5 #26042902

order11660
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productC4×C53×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C53)
unambiguous semidirect product(C4×C11×C53)⋊C5

Splittings

Fitting, HallC4×C11×C53 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C53
HallC11×C53 ⋊ C4×C5
HallC4×C11 ⋊ C5×C53

Subgroups

subgroupG/H
center, hypercenterC4×C53C11⋊C5
commutator, hypocenterC11C4×C5×C53
FrattiniC2C2×C53×C11⋊C5
FittingC4×C11×C53C5
socleC2×C11×C53C2×C5
prime radicalC2×C53×C11⋊C5C2
cosocleC2×C11C2×C5×C53
LCSG ▷ C11
UCSC1 ◁ C4×C53

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C53×C11⋊C5, Dic3×C53×C11⋊C5
maximal normal subgroup ofC3×C4×C53×C11⋊C5
maximal quotient ofC3×C4×C53×C11⋊C5, Dic3×C53×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11660, 2);