Finite Group Databasebeta

C3×#10613938 #14413405

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

Aliases

direct productC3×#10613938

Splittings

HallC3×C5 ⋊ #2911
SylowC5 ⋊ C3×#2911

Subgroups

subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#117C2
socleC22×C3×C5C22×D4
prime radicalC24×C3×C5D4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#2911
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×#117

984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 139103);