Finite Group Databasebeta

← Prev (#14413409) Next (#14413411) →

C3×#10617409 #14413410

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10617409

Splittings

FittingC2×C3×C5×M16 ⋊ C4
HallC3×C5 ⋊ #2911
SylowC5 ⋊ C3×#2911

Subgroups

subgroupG/H
centerC3×C4C2×C4⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC2×C3×C5C22×C4⋊C4
prime radicalC23×C3×D5D4
cosocleC4×D5C24×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#2911
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×M16

984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 139108);