Finite Group Databasebeta

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C2×C3×C5×D109⋊C3 #34087142

order19620
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5×D109⋊C3
unambiguous semidirect productD109⋊(C2×C32×C5)
unambiguous semidirect product(C109⋊C3)⋊(C22×C3×C5)
unambiguous semidirect product(C2×D109)⋊(C32×C5)
unambiguous semidirect product(C2×C109⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C2×C3×D109)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D109)⋊C32
unambiguous semidirect product(C2×C3×C5×D109)⋊C3

Splittings

Fitting, socleC2×C3×C5×C109 ⋊ C2×C3
derived, SylowC109 ⋊ C22×C32×C5
HallC3×C5×C109⋊C3 ⋊ C22
HallC2×C5×D109 ⋊ C32
HallC3×C109⋊C3 ⋊ C22×C5
HallC5×C109 ⋊ C22×C32
HallC2×D109 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D109⋊C3
commutator, cosocle, hypocenterC109C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C109C2×C3
LCSG ▷ C109
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3270

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 110);