Finite Group Databasebeta

← Prev (#13035446) Next (#13035448) →

C2×#10604030 #13035447

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

Aliases

direct productC2×#10604030
unambiguous semidirect productD5⋊#1947

Splittings

FittingC2×C5×C4⋊C8 ⋊ C4
SylowC5 ⋊ C2×#1947

Subgroups

subgroupG/H
centerC23C2×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC23×C5C2×C4⋊C4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5C2×#1947
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105715);