Finite Group Databasebeta

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C3×C5×C13×C22⋊(C13⋊C3) #44478331

order30420
automorphism?
homologyAbelianization (H1) = C32×C5×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×C13×C22⋊(C13⋊C3)
unambiguous semidirect product(C22×C3)⋊(C5×C13×C13⋊C3)
unambiguous semidirect product(C3×C13)⋊(C5×A4×C13)
unambiguous semidirect product(C22×C3×C5)⋊(C13×C13⋊C3)
unambiguous semidirect product(C3×C5×C13)⋊(A4×C13)

Splittings

Fitting, socleC22×C3×C5×C132 ⋊ C3
derivedC22×C13 ⋊ C32×C5×C13
HallC22×C5×C132 ⋊ C32
HallC5×C132 ⋊ C3×A4
HallC22×C132 ⋊ C32×C5
SylowC132 ⋊ C3×C5×A4
HallC22×C5 ⋊ C3×C13×C13⋊C3
SylowC22 ⋊ C3×C5×C13×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C32×C5×C13
FrattiniC1G
Fitting, socleC22×C3×C5×C132C3
LCSG ▷ C22×C13
UCSC1 ◁ C3×C5×C13

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1170

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 920);