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D5⋊C64 #10598483

order640
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C64 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD5⋊C64

Splittings

derived, SylowC5 ⋊ C2×C64

Subgroups

subgroupG/H
center, hypercenterC32AGL(1,𝔽5)
commutator, hypocenterC5C2×C64
FrattiniC16C2×AGL(1,𝔽5)
FittingC5×C32C4
socleC2×C5C2×C32
prime radicalC2×D5C32
cosocle#3926C22
LCSG ▷ C5
UCSC1 ◁ C32

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^7,5|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^2,h^b=h^4,h^c=h^4

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C64, #13014519, #13014584, …
maximal normal subgroup ofAGL(1,𝔽5)×C64, #13014519, #13014584, …
maximal quotient of#13014518, #13014527, #13014593, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 565);