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C22⋊AGL(1,ℤ/25) #14522338

order2000
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22

Aliases

unambiguous semidirect productC22⋊AGL(1,ℤ/25)
unambiguous semidirect product(C22⋊#1035)⋊C5
unambiguous semidirect product(C2×AGL(1,ℤ/25))⋊C2

Splittings

FittingC22×5−1+2 ⋊ C4
Sylow5−1+2 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC2C2×AGL(1,ℤ/25)
commutatorC2×C25C2×C4×C5
Frattini, socleC2×C5C2×C5×AGL(1,𝔽5)
FittingC22×5−1+2C4
prime radicalC22×D25⋊C5C2
cosocleC2×D25C22×C5
hypercenterC22AGL(1,ℤ/25)
hypocenterC25C5×C22⋊C4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C22

107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 100

Polycyclic presentation:

2^2,5,2^2,5^2|a^2=d,f^5=g,b^a=be,f^a=f^2g,g^a=g^2,f^c=fg,f^d=f^4g^4,g^d=g^4

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,ℤ/25), #72228881, C2×C22⋊AGL(1,ℤ/25), …
maximal normal subgroup ofD4×AGL(1,ℤ/25), C2×C22⋊AGL(1,ℤ/25), #72275737, …
maximal quotient ofC2×C22⋊AGL(1,ℤ/25), #72275610, #72275762, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 301);