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C4×AGL(1,ℤ/25) #14522325

order2000
isoclinismisoclinic class of AGL(1,ℤ/25)
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C4

Aliases

direct productC4×AGL(1,ℤ/25)
unambiguous semidirect product#1035⋊(C4×C5)
unambiguous semidirect product(C4×#1035)⋊C5

Splittings

FittingC4×5−1+2 ⋊ C4
derivedC25 ⋊ C42×C5
Sylow5−1+2 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,ℤ/25)
commutator, hypocenterC25C42×C5
Frattini, socleC2×C5C2×C5×AGL(1,𝔽5)
FittingC4×5−1+2C4
prime radicalC2×D25⋊C5C22
cosocleC2×D25C22×C5
LCSG ▷ C25
UCSC1 ◁ C4

93 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 100

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×AGL(1,ℤ/25), C3×C4×AGL(1,ℤ/25), C2×C4×AGL(1,ℤ/25), …
maximal normal subgroup ofC4×C5×AGL(1,ℤ/25), C3×C4×AGL(1,ℤ/25), C2×C4×AGL(1,ℤ/25), …
maximal quotient ofC4×C5×AGL(1,ℤ/25), C3×C4×AGL(1,ℤ/25), C2×C4×AGL(1,ℤ/25), …
automorphism group ofC5×D25, #87709, C5×#1035

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 288);