Finite Group Databasebeta

C22×C3×#4082 #14479657

order1920
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×C3×#4082

Splittings

HallC3×C5 ⋊ C22×#124
SylowC5 ⋊ C22×C3×#124

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
Fitting, prime radicalC23×C3×C5×D4C2
socleC24×C3×C5C23
hypercenterC23×C3×D4D5
hypocenterC5C22×C3×#124
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C23×C3×D4

3760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 205355);