Finite Group Databasebeta

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C2×C3×C4×AGL(1,ℤ/25) #72219044

order12000
isoclinismisoclinic class of AGL(1,ℤ/25)
automorphism?
homologyAbelianization (H1) = C2×C3×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C3×C4×AGL(1,ℤ/25)

Splittings

FittingC2×C3×C4×5−1+2 ⋊ C4
derivedC25 ⋊ C2×C3×C42×C5
HallC3×5−1+2 ⋊ C2×C42
Sylow5−1+2 ⋊ C2×C3×C42

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4AGL(1,ℤ/25)
commutator, hypocenterC25C2×C3×C42×C5
FrattiniC2×C5C22×C3×C5×AGL(1,𝔽5)
FittingC2×C3×C4×5−1+2C4
socleC22×C3×C5C2×C5×AGL(1,𝔽5)
prime radicalC22×C3×D25⋊C5C22
cosocleC2×D25C23×C3×C5
LCSG ▷ C25
UCSC1 ◁ C2×C3×C4

664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

624 conjugacy classes. The character table is too large to display.

Relationships

automorphism group ofC5×C7×D25

GAP

Past the SmallGroups library coverage — no SmallGroups id.