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C43⋊AGL(1,𝔽5) #11720023

order860
isoclinismisoclinic class of C43⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC43⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C43 ⋊ C4
SylowC43 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic43

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C43C4
prime radical, cosocleD5×C43C2
LCSG ▷ C5×C43
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 215

Polycyclic presentation:

2^2,5,43|a^2=b,c^a=c^3,d^a=d^42,c^b=c^4

Conjugacy classes & character table

89 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×D43, C2×C43⋊AGL(1,𝔽5), (C43⋊C3)⋊AGL(1,𝔽5), …
maximal normal subgroup ofAGL(1,𝔽5)×D43, C2×C43⋊AGL(1,𝔽5), (C43⋊C3)⋊AGL(1,𝔽5), …
maximal quotient ofC43⋊#170, C2×C43⋊AGL(1,𝔽5), C3×C43⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(860, 6);