Finite Group Databasebeta

C3×#10602212 #14312641

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#10602212

Splittings

HallC3×C5 ⋊ #2108
SylowC5 ⋊ C3×#2108

Subgroups

subgroupG/H
centerC2×C3×C8C22×D5
commutatorC2×C5C2×C3×C4×C8
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×M32C2
socleC22×C3×C5C22×C8
prime radicalC23×C3×C5C2×C8
cosocleC2×C5×C8C23×C3
hypercenterC2×C3×M32D5
hypocenterC5C3×#2108
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×M32

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38339);