Finite Group Databasebeta

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C3×D5×D109⋊C3 #34087126

order19620
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×D5×D109⋊C3
unambiguous semidirect productD109⋊(C32×D5)
unambiguous semidirect product(D5×D109)⋊C32
unambiguous semidirect product(C5×D109⋊C3)⋊(C2×C3)
unambiguous semidirect product(D5×C109⋊C3)⋊(C2×C3)
unambiguous semidirect product(C5⋊(D109⋊C3))⋊(C2×C3)
unambiguous semidirect product(C3×D5×D109)⋊C3

Splittings

Fitting, socleC3×C5×C109 ⋊ C22×C3
derived, HallC5×C109 ⋊ C22×C32
HallC3×C5×C109⋊C3 ⋊ C22
HallD5×D109 ⋊ C32
HallC3×C109⋊C3 ⋊ C2×D5
SylowC109 ⋊ C2×C32×D5
SylowC5 ⋊ C2×C3×D109⋊C3

Subgroups

subgroupG/H
center, hypercenterC3D5×D109⋊C3
commutator, cosocle, hypocenterC5×C109C22×C32
FrattiniC1G
Fitting, socleC3×C5×C109C22×C3
LCSG ▷ C5×C109
UCSC1 ◁ C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1635

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 94);