Finite Group Databasebeta

← Prev (#13093752) Next (#13093754) →

C3⋊AGL(1,ℤ/25) #13093753

order1500
isoclinismisoclinic class of C3⋊AGL(1,ℤ/25)
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊AGL(1,ℤ/25)
unambiguous semidirect product(C3⋊#1035)⋊C5

Splittings

Fitting, HallC3×5−1+2 ⋊ C4
derivedC3×C25 ⋊ C4×C5
Sylow5−1+2 ⋊ Dic3
SylowC3 ⋊ AGL(1,ℤ/25)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC3×C25C4×C5
FrattiniC5C5×ΓL(1,𝔽16)
FittingC3×5−1+2C4
socleC3×C5C5×AGL(1,𝔽5)
prime radicalC3×D25⋊C5C2
cosocleC3×D25C2×C5
LCSG ▷ C3×C25
UCSC1

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 75

Polycyclic presentation:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,ℤ/25), #72228881, #72241628, …
maximal normal subgroup ofD3×AGL(1,ℤ/25), C2×C3⋊AGL(1,ℤ/25), C3×C3⋊AGL(1,ℤ/25)
maximal quotient of#72228881, #72241628, C2×C3⋊AGL(1,ℤ/25), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1500, 54);