Finite Group Databasebeta

← Prev (#14417991) Next (#14417993) →

C2×#11751978 #14417992

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11751978

Splittings

HallC3×C5 ⋊ C2×#444
SylowC5 ⋊ C2×#5145
SylowC3 ⋊ C2×#65741

Subgroups

subgroupG/H
centerC22AGL(1,𝔽5)×#67
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×#91516C2
cosocleC3×C4×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143690);