Finite Group Databasebeta

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C3×C5×C13⋊C3×C43 #38737689

order25155
automorphism?
homologyAbelianization (H1) = C32×C5×C43 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C13⋊C3×C43
unambiguous semidirect productC13⋊(C32×C5×C43)
unambiguous semidirect product(C3×C13)⋊(C3×C5×C43)
unambiguous semidirect product(C5×C13)⋊(C32×C43)
unambiguous semidirect product(C3×C5×C13)⋊(C3×C43)

Splittings

Fitting, socleC3×C5×C13×C43 ⋊ C3
derived, SylowC13 ⋊ C32×C5×C43
HallC5×C13×C43 ⋊ C32
HallC13×C43 ⋊ C32×C5
HallC5×C13 ⋊ C32×C43

Subgroups

subgroupG/H
center, hypercenterC3×C5×C43C13⋊C3
commutator, cosocle, hypocenterC13C32×C5×C43
FrattiniC1G
Fitting, socleC3×C5×C13×C43C3
LCSG ▷ C13
UCSC1 ◁ C3×C5×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

4515 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25155, 9);