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C4×C5⋊AGL(1,ℤ/9) #11761867

order1080
isoclinismisoclinic class of C5⋊AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×C5⋊AGL(1,ℤ/9)
unambiguous semidirect product(C4×D45)⋊C3

Splittings

FittingC4×C5×3−1+2 ⋊ C2
derivedC5×C9 ⋊ C2×C3×C4
HallC5×3−1+2 ⋊ C2×C4
Sylow3−1+2 ⋊ C4×D5
SylowC5 ⋊ C4×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC4C5⋊AGL(1,ℤ/9)
commutator, hypocenterC5×C9C2×C3×C4
FrattiniC2×C3C2×C3×D15
FittingC4×C5×3−1+2C2
socleC2×C3×C5C2×C3×D3
prime radicalC2×C5⋊AGL(1,ℤ/9)C2
cosocleC2×C5×C9C22×C3
LCSG ▷ C5×C9
UCSC1 ◁ C4

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D5×AGL(1,ℤ/9), D4×C5⋊AGL(1,ℤ/9), #72247420, …
maximal normal subgroup ofC4×D5×AGL(1,ℤ/9), D4×C5⋊AGL(1,ℤ/9), #72247420
maximal quotient ofAGL(1,𝔽5)×C5⋊AGL(1,ℤ/9), #72254576

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 213);