Finite Group Databasebeta

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C22×C3×#4043 #14479424

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

Aliases

direct productC22×C3×#4043

Splittings

FittingC22×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ C22×C22⋊Q8
SylowC5 ⋊ C22×C3×C22⋊Q8

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5C23
prime radicalC24×C3×D5C22
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C22×C3×C22⋊Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

3680 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, 205122);