Finite Group Databasebeta

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C22×C5×#940 #14479961

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C5×#940

Splittings

FittingC23×C3×C5×D4 ⋊ C2
HallC3×C5 ⋊ C22×#127
SylowC3 ⋊ C22×C5×#127

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC23×C3×C5×D4C2
socleC24×C3×C5C23
hypercenterC23×C5×D4D3
hypocenterC3C22×C5×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C23×C5×D4

6000 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, 205659);