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C32×C11⋊AGL(1,𝔽5) #14520449

order1980
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C32×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C11 ⋊ C4
derived, HallC5×C11 ⋊ C32×C4
HallC32×C11 ⋊ AGL(1,𝔽5)
HallC32×C5 ⋊ Dic11
SylowC11 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C32×Dic11

Subgroups

subgroupG/H
center, hypercenterC32C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C32×C4
FrattiniC1G
Fitting, socleC32×C5×C11C4
prime radicalC32×D5×C11C2
cosocleD5×C11C2×C32
LCSG ▷ C5×C11
UCSC1 ◁ C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 495

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20,21,22);(4,5,6)(7,8,10,12,14,16,17,15,13,11,9)(18,19,22,20,21)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3×ΓL(1,𝔽8)×C11⋊AGL(1,𝔽5), C32×C7×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC32×C7×C11⋊AGL(1,𝔽5), C32×C11×C11⋊AGL(1,𝔽5), C32×C13×C11⋊AGL(1,𝔽5), …
maximal quotient ofC3×C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3×ΓL(1,𝔽8)×C11⋊AGL(1,𝔽5), C32×C7×C11⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 74);