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C32×C4×C11⋊C5 #14520419

order1980
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C4×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C32×C5)
unambiguous semidirect product(C3×C4×C11)⋊(C3×C5)
unambiguous semidirect product(C32×C4×C11)⋊C5

Splittings

Fitting, HallC32×C4×C11 ⋊ C5
derived, SylowC11 ⋊ C32×C4×C5
HallC32×C11 ⋊ C4×C5
HallC4×C11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32×C4C11⋊C5
commutator, hypocenterC11C32×C4×C5
FrattiniC2C2×C32×C11⋊C5
FittingC32×C4×C11C5
socleC2×C32×C11C2×C5
prime radicalC2×C32×C11⋊C5C2
cosocleC2×C11C2×C32×C5
LCSG ▷ C11
UCSC1 ◁ C32×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 396

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,3)(7,8,9,10)(12,13,15,18,17)(14,16,20,21,19);(4,5,6)(11,12,14,17,13,15,19,21,16,18,20)

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×ΓL(1,𝔽8)⋊C4, C3×C4×ΓL(1,𝔽8)×C11⋊C5, C32×Dic7×C11⋊C5, …
maximal normal subgroup ofC32×C4×C7×C11⋊C5, C32×C4×C11×C11⋊C5, C32×C4×C13×C11⋊C5, …
maximal quotient ofC3×C11⋊C5×ΓL(1,𝔽8)⋊C4, C3×C4×ΓL(1,𝔽8)×C11⋊C5, C32×Dic7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 44);