Finite Group Databasebeta

← Prev (#13043360) Next (#13043362) →

C2×D5⋊#361 #13043361

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊#361
unambiguous semidirect productD5⋊(C2×#361)

Splittings

SylowC5 ⋊ C22×#361

Subgroups

subgroupG/H
centerC22C2×#4007
commutatorC5×C8C23×C4
FrattiniC8C23×AGL(1,𝔽5)
FittingC22×C5×D8C4
socleC22×C5C2×#102
prime radicalC22×D5×D8C2
cosocleC8×D5C24
hypercenterC22×D8AGL(1,𝔽5)
hypocenterC5C22×#361
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#361, C2×D5⋊AGL(1,ℤ/16), C2×#13025910
maximal normal subgroup ofC2×AGL(1,𝔽5)×#361, C2×D5⋊AGL(1,ℤ/16), C2×#13025910

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113629);