Finite Group Databasebeta

← Prev (#14319804) Next (#14319806) →

C2×C3×#65800 #14319805

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×#65800
unambiguous semidirect productD5⋊(C3×#379)

Splittings

FittingC25×C3×C5 ⋊ C4
HallC3×C5 ⋊ C2×#379
SylowC5 ⋊ C2×C3×#379

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC25×C3×C5C4
socleC23×C3×C5C22×C4
prime radicalC25×C3×D5C2
cosocleC22×D5C24×C3
hypercenterC25×C3AGL(1,𝔽5)
hypocenterC5C2×C3×#379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C25×C3

6928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×#120, AGL(1,𝔽7)×#65800
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×#120
maximal quotient ofAGL(1,𝔽7)×#65800

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45503);