Finite Group Databasebeta

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C4×D3×AGL(1,𝔽31) #72219367

order22320
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC4×D3×AGL(1,𝔽31)

Splittings

FittingC3×C4×C31 ⋊ C22×C3×C5
derivedC3×C31 ⋊ C22×C3×C4×C5
HallC4×D3×D31⋊C3 ⋊ C5
HallC3×(C31⋊C3)⋊C5 ⋊ C22×C4
HallC3×C31⋊C3 ⋊ C22×C4×C5
HallΓL(1,𝔽32) ⋊ C2×C3×C4×D3
SylowC31 ⋊ C2×C3×C4×C5×D3

Subgroups

subgroupG/H
center, hypercenterC4D3×AGL(1,𝔽31)
commutator, hypocenterC3×C31C22×C3×C4×C5
FrattiniC2C2×D3×AGL(1,𝔽31)
FittingC3×C4×C31C22×C3×C5
socle, cosocleC2×C3×C31C23×C3×C5
prime radicalC2×D3×AGL(1,𝔽31)C2
LCSG ▷ C3×C31
UCSC1 ◁ C4

464 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C4×D3×AGL(1,𝔽31)
maximal normal subgroup ofC2×C4×D3×AGL(1,𝔽31)
maximal quotient ofC2×C4×D3×AGL(1,𝔽31)

GAP

Past the SmallGroups library coverage — no SmallGroups id.