Finite Group Databasebeta

← Prev (#14522325) Next (#14522327) →

C4⋊AGL(1,ℤ/25) #14522326

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

Aliases

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

Splittings

FittingC4×5−1+2 ⋊ C4
Sylow5−1+2 ⋊ C4⋊C4

Subgroups

subgroupG/H
centerC2C2×AGL(1,ℤ/25)
commutatorC2×C25C2×C4×C5
Frattini, socleC2×C5C2×C5×AGL(1,𝔽5)
FittingC4×5−1+2C4
prime radicalC2×D25⋊C5C22
cosocleC2×D25C22×C5
hypercenterC4AGL(1,ℤ/25)
hypocenterC25C5×C4⋊C4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C4

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 100

Polycyclic presentation:

2^2,5,2^2,5^2|a^2=d,b^2=e,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), C2×C4⋊AGL(1,ℤ/25), #72275737, …
maximal normal subgroup ofD4×AGL(1,ℤ/25), C2×C4⋊AGL(1,ℤ/25), #72275737, …
maximal quotient ofC2×C4⋊AGL(1,ℤ/25), #72275610, #72275758, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 289);