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D5⋊(D5⋊AGL(1,𝔽5)) #14522953

order2000
isoclinismisoclinic class of D5⋊(D5⋊AGL(1,𝔽5))
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

unambiguous semidirect productD5⋊(D5⋊AGL(1,𝔽5))
unambiguous semidirect product(D5⋊#1043)⋊C2

Splittings

Fitting, socle, derived, SylowC53 ⋊ C22×C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC53C22×C4
prime radicalD53C2
cosocleC5⋊(C5⋊D5)C23
LCSG ▷ C53
UCSC1

336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20

Polycyclic presentation:

2^4,5^3|a^2=d,e^a=e^2,f^a=f^2,g^a=g^2,f^b=f^4,e^c=e^4,e^d=e^4,f^d=f^4,g^d=g^4

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×D5⋊AGL(1,𝔽5), C2×D5⋊(D5⋊AGL(1,𝔽5)), #72259565, …
maximal normal subgroup ofAGL(1,𝔽5)×D5⋊AGL(1,𝔽5), C2×D5⋊(D5⋊AGL(1,𝔽5)), C3×D5⋊(D5⋊AGL(1,𝔽5))
maximal quotient of#72228944, #72228966, C2×D5⋊(D5⋊AGL(1,𝔽5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 916);