Finite Group Databasebeta

← Prev (#14520394) Next (#14520396) →

C9×C11⋊AGL(1,𝔽5) #14520395

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

Aliases

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

Splittings

Fitting, HallC5×C9×C11 ⋊ C4
derived, HallC5×C11 ⋊ C4×C9
HallC9×C11 ⋊ AGL(1,𝔽5)
HallC5×C9 ⋊ Dic11
SylowC11 ⋊ C9×AGL(1,𝔽5)
SylowC5 ⋊ C9×Dic11

Subgroups

subgroupG/H
center, hypercenterC9C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C9
FrattiniC3C3×C11⋊AGL(1,𝔽5)
FittingC5×C9×C11C4
socleC3×C5×C11C3×C4
prime radical, cosocleC3×D5×C11C2×C3
LCSG ▷ C5×C11
UCSC1 ◁ C9

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)(11,12)(13,14)(15,16)(17,18)(19,20)(22,23,24,25);(10,11,13,15,17,19,20,18,16,14,12)(21,22,25,23,24)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊((C7⋊C9)⋊AGL(1,𝔽5)), C7⋊C9×C11⋊AGL(1,𝔽5), C7×C9×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC7×C9×C11⋊AGL(1,𝔽5), C9×C11×C11⋊AGL(1,𝔽5), C9×C13×C11⋊AGL(1,𝔽5), …
maximal quotient ofC11⋊((C7⋊C9)⋊AGL(1,𝔽5)), C7⋊C9×C11⋊AGL(1,𝔽5), C7×C9×C11⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 20);