Finite Group Databasebeta

C3×#10617554 #14412210

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10617554

Splittings

HallC3×C5 ⋊ #2889
SylowC5 ⋊ C3×#2889

Subgroups

subgroupG/H
centerC2×C3C22×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×#4150C2
cosocleC2×Dic5C24×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C3×#2889
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×D4 ◁ C2×C3×#41

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137908);