Finite Group Databasebeta

C2×C3×#66159 #14480465

order1920
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×#66159

Splittings

HallC3×C5 ⋊ C2×#536
SylowC5 ⋊ C2×C3×#536

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
Fitting, prime radicalC22×C3×C5×#41C2
socleC23×C3×C5C24
hypercenterC22×C3×#41D5
hypocenterC5C2×C3×#536
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×#41

3024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 206163);