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C9×C11×AGL(1,𝔽5) #14520394

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

Aliases

direct productC9×C11×AGL(1,𝔽5)

Splittings

Fitting, HallC5×C9×C11 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C11
HallC5×C11 ⋊ C4×C9
HallC5×C9 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC9×C11AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C11
FrattiniC3C3×C11×AGL(1,𝔽5)
FittingC5×C9×C11C4
socleC3×C5×C11C3×C4
prime radicalC3×D5×C11C2×C3
cosocleC3×D5C2×C3×C11
LCSG ▷ C5
UCSC1 ◁ C9×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)(10,11,12,13,14,15,16,17,18,19,20)(22,23,24,25);(21,22,23,25,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×(C7⋊C9)⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)×C7⋊C9, C7×C9×C11×AGL(1,𝔽5), …
maximal normal subgroup ofC7×C9×C11×AGL(1,𝔽5), C9×AGL(1,𝔽5)×C121, C9×C112×AGL(1,𝔽5), …
maximal quotient ofC11×(C7⋊C9)⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)×C7⋊C9, C7×C9×C11×AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 19);