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AGL(1,𝔽47) #14524181

order2162
isoclinismisoclinic class of AGL(1,𝔽47)
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

affine general linearAGL(1,𝔽47)
unambiguous semidirect productD47⋊C23
unambiguous semidirect product(C47⋊C23)⋊C2

Splittings

Fitting, socle, derived, SylowC47 ⋊ C2×C23
HallC47⋊C23 ⋊ C2
HallD47 ⋊ C23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC47C2×C23
LCSG ▷ C47
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 47

Polycyclic presentation:

2,23,47|c^a=c^46,c^b=c^25

Conjugacy classes & character table

47 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽47), C5×AGL(1,𝔽47), C5⋊AGL(1,𝔽47), …
maximal normal subgroup ofC2×AGL(1,𝔽47), C5×AGL(1,𝔽47), C7×AGL(1,𝔽47), …
maximal quotient ofDic47⋊C23, C2×AGL(1,𝔽47), C5×AGL(1,𝔽47), …
automorphism group ofD47
holomorph ofC47

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2162, 1);