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D5⋊#674 #11716774

order800
isoclinismisoclinic class of D5⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C16 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD5⋊#674

Splittings

derived, SylowC52 ⋊ C2×C16

Subgroups

subgroupG/H
center, Frattini, hypercenterC4D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C2×C16
FittingC4×C52C2×C4
socleC2×C52C2×C8
prime radicalC2×C5×D5C8
cosocle#6029C22
LCSG ▷ C52
UCSC1 ◁ C4

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Polycyclic presentation:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#674, #13103265, #13103268, …
maximal normal subgroup ofAGL(1,𝔽5)×#674, #13103265, #13103268, …
maximal quotient ofD5⋊#3928, #13099873, #13099918, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(800, 433);