Finite Group Databasebeta

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C22×C3×#3941 #14412245

order1920
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C3×#3941

Splittings

FittingC22×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ C22×#102
SylowC5 ⋊ C22×C3×#102

Subgroups

subgroupG/H
centerC24×C3C22⋊D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5D4
prime radicalC23×C3×D20C2
cosocleC2×C4×C5C24×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C22×C3×#102
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

2144 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, 137943);