Finite Group Databasebeta

C22×C4×#1200 #14478672

order1920
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×#1200

Splittings

derived, HallC3×C5 ⋊ C23×C42
SylowC5 ⋊ C22×C42×D3
SylowC3 ⋊ C22×C42×D5

Subgroups

subgroupG/H
center, hypercenterC23×C4D3×D5
commutator, hypocenterC3×C5C23×C42
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×D15C22
cosocleC22×C3×C5C25
LCSG ▷ C3×C5
UCSC1 ◁ C23×C4

6000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204370);