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3−1+2⋊AGL(1,𝔽5) #10587378

order540
isoclinismisoclinic class of 3−1+2⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product3−1+2⋊AGL(1,𝔽5)
unambiguous semidirect product(C9⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, HallC5×3−1+2 ⋊ C4
derivedC5×C9 ⋊ C3×C4
Sylow3−1+2 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ 3−1+2⋊C4

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC5×C9C3×C4
FrattiniC3C3×ΓL(1,𝔽16)
FittingC5×3−1+2C4
socleC3×C5C3×Dic3
prime radicalC32×D5D3
cosocleC9×D5C2×C3
LCSG ▷ C5×C9
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 45

Polycyclic presentation:

2,3,2,3,5,3|a^2=c,d^3=f^2,d^a=d^2f,e^a=e^3,f^a=f^2,d^b=df,e^c=e^4

Conjugacy classes & character table

31 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/9), C2×3−1+2⋊AGL(1,𝔽5), #13108191, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/9), C2×3−1+2⋊AGL(1,𝔽5), C3×3−1+2⋊AGL(1,𝔽5), …
maximal quotient of3−1+2⋊#170, C2×3−1+2⋊AGL(1,𝔽5), #13108177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 38);