Finite Group Databasebeta

← Prev (#13034783) Next (#13034785) →

C2×#10604003 #13034784

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

Aliases

direct productC2×#10604003
unambiguous semidirect productD5⋊#1859

Splittings

FittingC2×C5×#104 ⋊ C4
SylowC5 ⋊ C2×#1859

Subgroups

subgroupG/H
centerC22#65699
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#104C4
socleC22×C5#385
prime radicalC2×D5×#41C22
cosocleC2×C4×D5C24
hypercenterC2×#104AGL(1,𝔽5)
hypocenterC5C2×#1859
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

1566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221210, C2×#72213383, C2×AGL(1,𝔽5)×#453, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#453, #72221485, #72221519, …
maximal quotient ofC2×#72221210, C2×#72213383, D3×#10604003, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105052);