Finite Group Databasebeta

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C571⋊AGL(1,𝔽5) #26037658

order11420
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC571⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C571 ⋊ C4
SylowC571 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic571

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C571C4
prime radical, cosocleD5×C571C2
LCSG ▷ C5×C571
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,571|a^2=b,c^a=c^2,d^a=d^570,c^b=c^4

Conjugacy classes & character table

1145 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C571⋊C3)⋊AGL(1,𝔽5), C3×C571⋊AGL(1,𝔽5), C3⋊(C571⋊AGL(1,𝔽5))
maximal normal subgroup of(C571⋊C3)⋊AGL(1,𝔽5), C3×C571⋊AGL(1,𝔽5)
maximal quotient ofC3×C571⋊AGL(1,𝔽5), C3⋊(C571⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11420, 11);