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C5×C3⋊AGL(1,𝔽43) #41029124

order27090
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊AGL(1,𝔽43)
unambiguous semidirect productC3⋊(C5×AGL(1,𝔽43))
unambiguous semidirect product(C3⋊(D43⋊C3))⋊(C5×C7)
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C5×D3)
unambiguous semidirect product(C3⋊(D43⋊C7))⋊(C3×C5)
unambiguous semidirect product(C5×C3⋊(D43⋊C3))⋊C7
unambiguous semidirect product(C5×C3⋊(D43⋊C7))⋊C3

Splittings

Fitting, socleC3×C5×C43 ⋊ C2×C3×C7
derivedC3×C43 ⋊ C2×C3×C5×C7
HallC3×C5×(C43⋊C3)⋊C7 ⋊ C2
HallC5×C3⋊(D43⋊C3) ⋊ C7
HallC3×(C43⋊C3)⋊C7 ⋊ C2×C5
HallC3×C5×C43⋊C3 ⋊ C2×C7
HallC5×C43⋊C7 ⋊ C3×D3
HallC3⋊(D43⋊C3) ⋊ C5×C7
HallC3×C43⋊C3 ⋊ C2×C5×C7
HallC43⋊C7 ⋊ C3×C5×D3
HallC5×C43 ⋊ C3×D3×C7
SylowC43 ⋊ C3×C5×D3×C7

Subgroups

subgroupG/H
center, hypercenterC5C3⋊AGL(1,𝔽43)
commutator, cosocle, hypocenterC3×C43C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C43C2×C3×C7
LCSG ▷ C3×C43
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 645

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27090, 65);