Finite Group Databasebeta

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D3×AGL(1,𝔽7)×C127 #44544818

order32004
automorphism?
homologyAbelianization (H1) = C22×C3×C127 · Schur multiplier (H2) = C2

Aliases

direct productD3×AGL(1,𝔽7)×C127
unambiguous semidirect productD7⋊(C3×D3×C127)
unambiguous semidirect product(D3×D7)⋊(C3×C127)
unambiguous semidirect product(C3×AGL(1,𝔽7))⋊(C2×C127)
unambiguous semidirect product(D3×ΓL(1,𝔽8))⋊(C2×C127)
unambiguous semidirect product(C3⋊AGL(1,𝔽7))⋊(C2×C127)

Splittings

Fitting, socleC3×C7×C127 ⋊ C22×C3
derivedC3×C7 ⋊ C22×C3×C127
HallC3×ΓL(1,𝔽8)×C127 ⋊ C22
HallC7×C127 ⋊ C2×C3×D3
HallC3×ΓL(1,𝔽8) ⋊ C22×C127
SylowC7 ⋊ C2×C3×D3×C127

Subgroups

subgroupG/H
center, hypercenterC127D3×AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C7C22×C3×C127
FrattiniC1G
Fitting, socleC3×C7×C127C22×C3
LCSG ▷ C3×C7
UCSC1 ◁ C127

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2667

Conjugacy classes & character table

2667 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 200);