Finite Group Databasebeta

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C3×D3×D7×AGL(1,𝔽5) #72218039

order5040
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D3×D7×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC32×C5×C7 ⋊ C22×C4
derivedC3×C5×C7 ⋊ C22×C3×C4
HallC32×C7 ⋊ C22×AGL(1,𝔽5)
HallC32×C5 ⋊ C2×C4×D7
HallC5×C7 ⋊ C2×C3×C4×D3
SylowC32 ⋊ C2×D7×AGL(1,𝔽5)
SylowC7 ⋊ C2×C3×D3×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×D3×D7

Subgroups

subgroupG/H
center, hypercenterC3D3×D7×AGL(1,𝔽5)
commutator, hypocenterC3×C5×C7C22×C3×C4
FrattiniC1G
Fitting, socleC32×C5×C7C22×C4
prime radicalC3×D3×D5×D7C2
cosocleC3×C7×D5C23×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3

464 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×AGL(1,𝔽5)×AGL(1,𝔽7), D32×D7×AGL(1,𝔽5)
maximal normal subgroup ofC3×D3×AGL(1,𝔽5)×AGL(1,𝔽7), D32×D7×AGL(1,𝔽5)

GAP

Past the SmallGroups library coverage — no SmallGroups id.