Finite Group Databasebeta

← Prev (#13034823) Next (#13034825) →

C2×#10603919 #13034824

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#10603919
unambiguous semidirect productD5⋊#1867

Splittings

FittingC2×C5×#99 ⋊ C4
SylowC5 ⋊ C2×#1867

Subgroups

subgroupG/H
centerC22#65699
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C5×#99C4
socleC22×C5#385
prime radicalC22×D4×D5C22
cosocleC23×D5C24
hypercenterC2×#99AGL(1,𝔽5)
hypocenterC5C2×#1867
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

1994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×B(4,𝔽2), D3×#10603919, #72242724, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×B(4,𝔽2), #72242724, #72242738, …
maximal quotient ofD3×#10603919, #72242744, #72242746, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105092);