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C47⋊AGL(1,𝔽5) #11745642

order940
isoclinismisoclinic class of C47⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC47⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C47 ⋊ C4
SylowC47 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic47

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C47C4
prime radical, cosocleD5×C47C2
LCSG ▷ C5×C47
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 235

Polycyclic presentation:

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

Conjugacy classes & character table

97 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×D47, C2×C47⋊AGL(1,𝔽5), C3×C47⋊AGL(1,𝔽5), …
maximal normal subgroup ofAGL(1,𝔽5)×D47, C2×C47⋊AGL(1,𝔽5), C3×C47⋊AGL(1,𝔽5), …
maximal quotient ofC47⋊#170, C2×C47⋊AGL(1,𝔽5), C3×C47⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(940, 6);