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C11×C9⋊AGL(1,𝔽5) #14520396

order1980
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(C11×AGL(1,𝔽5))

Splittings

Fitting, HallC5×C9×C11 ⋊ C4
derived, HallC5×C9 ⋊ C4×C11
HallC9×C11 ⋊ AGL(1,𝔽5)
HallC5×C11 ⋊ Dic9
SylowC9 ⋊ C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×Dic9

Subgroups

subgroupG/H
center, hypercenterC11C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C11
FrattiniC3C11×ΓL(1,𝔽16)
FittingC5×C9×C11C4
socleC3×C5×C11Dic3
prime radicalC3×D5×C11D3
cosocleC9×D5C2×C11
LCSG ▷ C5×C9
UCSC1 ◁ C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 495

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,15,16)(18,20)(19,23)(21,22)(24,25);(12,13,16,14,15)(17,25,20,23,22,21,19,18,24)

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11×C9⋊AGL(1,𝔽5), C11×C7⋊(C9⋊AGL(1,𝔽5)), C121×C9⋊AGL(1,𝔽5), …
maximal normal subgroup ofC7×C11×C9⋊AGL(1,𝔽5), C121×C9⋊AGL(1,𝔽5), C112×C9⋊AGL(1,𝔽5), …
maximal quotient ofC7×C11×C9⋊AGL(1,𝔽5), C11×C7⋊(C9⋊AGL(1,𝔽5)), C121×C9⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 21);