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C3×C5⋊AGL(1,𝔽47) #44569873

order32430
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5⋊AGL(1,𝔽47)
unambiguous semidirect productC5⋊(C3×AGL(1,𝔽47))
unambiguous semidirect productD235⋊(C3×C23)
unambiguous semidirect product(C47⋊C23)⋊(C3×D5)
unambiguous semidirect product(C3×D235)⋊C23

Splittings

Fitting, socle, HallC3×C5×C47 ⋊ C2×C23
derived, HallC5×C47 ⋊ C2×C3×C23
HallC3×C5×C47⋊C23 ⋊ C2
HallC5×C47⋊C23 ⋊ C2×C3
HallC3×C47⋊C23 ⋊ D5
HallC3×D235 ⋊ C23
HallC47⋊C23 ⋊ C3×D5
HallD235 ⋊ C3×C23
HallC3×C47 ⋊ D5×C23
SylowC47 ⋊ C3×D5×C23
HallC3×C5 ⋊ AGL(1,𝔽47)
SylowC5 ⋊ C3×AGL(1,𝔽47)

Subgroups

subgroupG/H
center, hypercenterC3C5⋊AGL(1,𝔽47)
commutator, cosocle, hypocenterC5×C47C2×C3×C23
FrattiniC1G
Fitting, socleC3×C5×C47C2×C23
LCSG ▷ C5×C47
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 705

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32430, 20);