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D3×AGL(1,𝔽7)×C149 #49176348

order37548
automorphism?
homologyAbelianization (H1) = C22×C3×C149 · Schur multiplier (H2) = C2

Aliases

direct productD3×AGL(1,𝔽7)×C149
unambiguous semidirect productD7⋊(C3×D3×C149)
unambiguous semidirect product(D3×D7)⋊(C3×C149)
unambiguous semidirect product(C3×AGL(1,𝔽7))⋊(C2×C149)
unambiguous semidirect product(D3×ΓL(1,𝔽8))⋊(C2×C149)
unambiguous semidirect product(C3⋊AGL(1,𝔽7))⋊(C2×C149)
unambiguous semidirect product(D3×D7×C149)⋊C3

Splittings

Fitting, socleC3×C7×C149 ⋊ C22×C3
derivedC3×C7 ⋊ C22×C3×C149
HallC3×ΓL(1,𝔽8)×C149 ⋊ C22
HallC7×C149 ⋊ C2×C3×D3
HallC3×ΓL(1,𝔽8) ⋊ C22×C149
SylowC7 ⋊ C2×C3×D3×C149

Subgroups

subgroupG/H
center, hypercenterC149D3×AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C7C22×C3×C149
FrattiniC1G
Fitting, socleC3×C7×C149C22×C3
LCSG ▷ C3×C7
UCSC1 ◁ C149

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3129

Conjugacy classes & character table

3129 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37548, 67);