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C71⋊AGL(1,𝔽5) #13083508

order1420
isoclinismisoclinic class of C71⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC71⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C71 ⋊ C4
SylowC71 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic71

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C71C4
prime radical, cosocleD5×C71C2
LCSG ▷ C5×C71
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 76
transitive degreeμt(G) = 355

Polycyclic presentation:

2^2,5,71|a^2=b,c^a=c^2,d^a=d^70,c^b=c^4

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C71⋊AGL(1,𝔽5), C3⋊(C71⋊AGL(1,𝔽5)), C71⋊#4380, …
maximal normal subgroup ofC3×C71⋊AGL(1,𝔽5), C11×C71⋊AGL(1,𝔽5), C13×C71⋊AGL(1,𝔽5), …
maximal quotient ofC3×C71⋊AGL(1,𝔽5), C3⋊(C71⋊AGL(1,𝔽5)), C71⋊#4380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1420, 10);