Finite Group Databasebeta

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C2×C3×C5×C42⋊C3 #13087786

order1440
isoclinismisoclinic class of C42⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3×C4

Aliases

direct productC2×C3×C5×C42⋊C3
unambiguous semidirect product(C2×C42)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C42)⋊(C3×C5)
unambiguous semidirect product(C2×C42×C5)⋊C32
unambiguous semidirect product(C2×C3×C42×C5)⋊C3

Splittings

FittingC2×C3×C42×C5 ⋊ C3
derivedC42 ⋊ C2×C32×C5
HallC2×C42×C5 ⋊ C32
SylowC2×C42 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C42⋊C3
commutator, cosocle, hypocenterC42C2×C32×C5
FrattiniC22C2×C3×C5×A4
FittingC2×C3×C42×C5C3
socleC23×C3×C5A4
LCSG ▷ C42
UCSC1 ◁ C2×C3×C5

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4103);