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D5⋊#435 #10617148

order640
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

unambiguous semidirect productD5⋊#435

Splittings

SylowC5 ⋊ C2×#435

Subgroups

subgroupG/H
centerC2×C4C22×AGL(1,𝔽5)
commutator, socleC22×C5C23×C4
FrattiniC22C23×AGL(1,𝔽5)
FittingC4×C5×D4C4
prime radicalC2×D4×D5C4
cosocleC2×Dic5C24
hypercenterC4×D4AGL(1,𝔽5)
hypocenterC5C2×#435
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×D4

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Polycyclic presentation:

2^7,5|a^2=f,c^2=f,f^2=g,b^a=be,c^a=cg,h^a=h^2,h^c=h^3,h^d=h^4,h^f=h^4

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13033720, AGL(1,𝔽5)×#435, #13033741, …
maximal normal subgroup of#13033720, AGL(1,𝔽5)×#435, #13033741, …
maximal quotient ofD5⋊#1581, D5⋊#1583, D5⋊#1582, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 19230);