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C59⋊AGL(1,𝔽5) #11924377

order1180
isoclinismisoclinic class of C59⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC59⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C59 ⋊ C4
SylowC59 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C59C4
prime radical, cosocleD5×C59C2
LCSG ▷ C5×C59
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 295

Polycyclic presentation:

2^2,5,59|a^2=b,c^a=c^2,d^a=d^58,c^b=c^4

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C59⋊AGL(1,𝔽5), C3⋊(C59⋊AGL(1,𝔽5)), C11×C59⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C59⋊AGL(1,𝔽5), C11×C59⋊AGL(1,𝔽5), C13×C59⋊AGL(1,𝔽5), …
maximal quotient ofC3×C59⋊AGL(1,𝔽5), C3⋊(C59⋊AGL(1,𝔽5)), C11×C59⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1180, 6);