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A5⋊AGL(1,𝔽5) #11925729

order1200
isoclinismisoclinic class of A5⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productA5⋊AGL(1,𝔽5)

Splittings

FittingC5 ⋊ A5⋊C4
socle, derivedC5×A5 ⋊ C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, hypocenterC5×A5C4
FittingC5A5⋊C4
prime radical, cosocleD5×A5C2
LCSG ▷ C5×A5
UCSC1

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25

Permutation generators:

(1,5,4,3,2)(6,10,9,8,7);(1,3)(6,7,9,8)

Conjugacy classes & character table

19 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72219548, AGL(1,𝔽5)×S5, C2×A5⋊AGL(1,𝔽5), …
maximal normal subgroup ofAGL(1,𝔽5)×S5, C2×A5⋊AGL(1,𝔽5), C3×A5⋊AGL(1,𝔽5)
maximal quotient of#72219547, C2×A5⋊AGL(1,𝔽5), C3×A5⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 939);