Finite Group Databasebeta

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C3×C5×C22⋊(C109⋊C3) #34087200

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

Aliases

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

Splittings

Fitting, socleC22×C3×C5×C109 ⋊ C3
derived, HallC22×C109 ⋊ C32×C5
HallC22×C5×C109 ⋊ C32
HallC5×C109 ⋊ C3×A4
SylowC109 ⋊ C3×C5×A4
HallC22×C5 ⋊ C3×C109⋊C3
SylowC22 ⋊ C3×C5×C109⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C109⋊C3)
commutator, cosocle, hypocenterC22×C109C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C109C3
LCSG ▷ C22×C109
UCSC1 ◁ C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

2220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 168);