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D3×AGL(1,ℤ/25) #72220602

order3000
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×AGL(1,ℤ/25)

Splittings

Fitting, HallC3×5−1+2 ⋊ C2×C4
derivedC3×C25 ⋊ C2×C4×C5
Sylow5−1+2 ⋊ C4×D3
SylowC3 ⋊ C2×AGL(1,ℤ/25)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC3×C25C2×C4×C5
FrattiniC5C5×D3×AGL(1,𝔽5)
FittingC3×5−1+2C2×C4
socleC3×C5C2×C5×AGL(1,𝔽5)
prime radicalD3×D25⋊C5C2
cosocleC3×D25C22×C5
LCSG ▷ C3×C25
UCSC1

100 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofS4×AGL(1,ℤ/25), C3⋊D3×AGL(1,ℤ/25), C2×D3×AGL(1,ℤ/25), …
maximal normal subgroup ofC2×D3×AGL(1,ℤ/25), C3×D3×AGL(1,ℤ/25)
maximal quotient ofS4×AGL(1,ℤ/25), C3⋊D3×AGL(1,ℤ/25), C2×D3×AGL(1,ℤ/25), …
automorphism group ofD75
holomorph ofC3×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.