Finite Group Databasebeta

← Prev (#14314083) Next (#14314085) →

C2×C3×#64708 #14314084

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×#64708

Splittings

FittingC2×C3×C5×#106 ⋊ C2
HallC3×C5 ⋊ C2×#360
SylowC5 ⋊ C2×C3×#360

Subgroups

subgroupG/H
centerC22×C3#3941
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×#106C2
socleC22×C3×C5#102
prime radicalC2×C3×#4050C2
cosocleC2×C5×C8C23×C3
hypercenterC2×C3×#106D5
hypocenterC5C2×C3×#360
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#106

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39782);