Finite Group Databasebeta

← Prev (#34087127) Next (#34087129) →

C5×D3×D109⋊C3 #34087128

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

Aliases

direct productC5×D3×D109⋊C3
unambiguous semidirect productD109⋊(C3×C5×D3)
unambiguous semidirect product(D3×D109)⋊(C3×C5)
unambiguous semidirect product(C3×D109⋊C3)⋊(C2×C5)
unambiguous semidirect product(D3×C109⋊C3)⋊(C2×C5)
unambiguous semidirect product(C3⋊(D109⋊C3))⋊(C2×C5)
unambiguous semidirect product(C5×D3×D109)⋊C3

Splittings

Fitting, socleC3×C5×C109 ⋊ C22×C3
derivedC3×C109 ⋊ C22×C3×C5
HallC3×C5×C109⋊C3 ⋊ C22
HallC3×C109⋊C3 ⋊ C22×C5
HallC5×C109 ⋊ C2×C3×D3
SylowC109 ⋊ C2×C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC5D3×D109⋊C3
commutator, cosocle, hypocenterC3×C109C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C109C22×C3
LCSG ▷ C3×C109
UCSC1 ◁ C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1635

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 96);