Finite Group Databasebeta

← Prev (#13110312) Next (#13110314) →

C83⋊AGL(1,𝔽5) #13110313

order1660
isoclinismisoclinic class of C83⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC83⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C83 ⋊ C4
SylowC83 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic83

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C83C4
prime radical, cosocleD5×C83C2
LCSG ▷ C5×C83
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 88
transitive degreeμt(G) = 415

Polycyclic presentation:

2^2,5,83|a^2=b,c^a=c^2,d^a=d^82,c^b=c^4

Conjugacy classes & character table

169 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C83⋊AGL(1,𝔽5), C7⋊(C83⋊AGL(1,𝔽5)), C83⋊#4380, …
maximal normal subgroup ofC7×C83⋊AGL(1,𝔽5), C11×C83⋊AGL(1,𝔽5), C13×C83⋊AGL(1,𝔽5), …
maximal quotient ofC7×C83⋊AGL(1,𝔽5), C7⋊(C83⋊AGL(1,𝔽5)), C83⋊#4380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1660, 6);