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C3×C5×AGL(1,𝔽9) #11762149

order1080
isoclinismisoclinic class of AGL(1,𝔽9)
automorphism?
homologyAbelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×AGL(1,𝔽9)

Splittings

Fitting, socle, HallC33×C5 ⋊ C8
derivedC32 ⋊ C3×C5×C8
SylowC33 ⋊ C5×C8

Subgroups

subgroupG/H
center, hypercenterC3×C5AGL(1,𝔽9)
commutator, hypocenterC32C3×C5×C8
FrattiniC1G
Fitting, socleC33×C5C8
prime radicalC3×C5×C3⋊D3C4
cosocle#157C2×C3×C5
LCSG ▷ C32
UCSC1 ◁ C3×C5

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×AGL(1,𝔽9), C2×C3×C5×AGL(1,𝔽9), C5×ΓL(1,𝔽8)×AGL(1,𝔽9), …
maximal normal subgroup ofC3×D5×AGL(1,𝔽9), C2×C3×C5×AGL(1,𝔽9), C3×C5×AΓL(1,𝔽9), …
maximal quotient ofC2×C3×C5×AGL(1,𝔽9), C5×ΓL(1,𝔽8)×AGL(1,𝔽9), C5×ΓL(1,𝔽8)⋊AGL(1,𝔽9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 495);