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C3⋊(C5⋊AGL(1,𝔽47)) #44569877

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

Aliases

unambiguous semidirect productC3⋊(C5⋊AGL(1,𝔽47))
unambiguous semidirect productC5⋊(C3⋊AGL(1,𝔽47))
unambiguous semidirect product(C47⋊C23)⋊D15
unambiguous semidirect productD705⋊C23

Splittings

Fitting, socle, derived, HallC3×C5×C47 ⋊ C2×C23
HallC3×C5×C47⋊C23 ⋊ C2
HallC5×C47⋊C23 ⋊ D3
HallC3×C47⋊C23 ⋊ D5
HallD705 ⋊ C23
HallC47⋊C23 ⋊ D15
HallC5×C47 ⋊ D3×C23
HallC3×C47 ⋊ D5×C23
SylowC47 ⋊ C23×D15
HallC3×C5 ⋊ AGL(1,𝔽47)
SylowC5 ⋊ C3⋊AGL(1,𝔽47)
SylowC3 ⋊ C5⋊AGL(1,𝔽47)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C47C2×C23
LCSG ▷ C3×C5×C47
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 705

Polycyclic presentation:

2,3,5,23,47|b^a=b^2,c^a=c^4,e^a=e^46,e^d=e^25

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32430, 24);