Finite Group Databasebeta

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C3×C5×A4×C109 #34087201

order19620
automorphism?
homologyAbelianization (H1) = C32×C5×C109 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×A4×C109
unambiguous semidirect productC22⋊(C32×C5×C109)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C109)
unambiguous semidirect product(C22×C5)⋊(C32×C109)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C109)

Splittings

Fitting, socleC22×C3×C5×C109 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C109
HallC22×C5×C109 ⋊ C32
HallC22×C109 ⋊ C32×C5
HallC22×C5 ⋊ C32×C109

Subgroups

subgroupG/H
center, hypercenterC3×C5×C109A4
commutator, cosocle, hypocenterC22C32×C5×C109
FrattiniC1G
Fitting, socleC22×C3×C5×C109C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C109

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

6540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 169);