Finite Group Databasebeta

C3×#10604861 #14315197

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10604861

Splittings

HallC3×C5 ⋊ #2170
SylowC5 ⋊ C3×#2170

Subgroups

subgroupG/H
centerC3×C4D4×AGL(1,𝔽5)
commutatorC4×C5C22×C3×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
Fitting, prime radicalC3×C5×#135C4
socleC2×C3×C5C8×D4
cosocleC2×#168C23×C3
hypercenterC3×#135AGL(1,𝔽5)
hypocenterC5C3×#2170
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#135

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40895);