Finite Group Databasebeta

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C5×C3⋊(#10621721⋊C3) #44477492

order30420
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(#10621721⋊C3)
unambiguous semidirect productC3⋊(C5×#10621721⋊C3)
unambiguous semidirect product(C3⋊#10621721)⋊(C3×C5)
unambiguous semidirect product(C5×C3⋊#10621721)⋊C3

Splittings

FittingC3×C5×C169 ⋊ C3×C4
derivedC3×C169 ⋊ C3×C4×C5
HallC3×C5×C169⋊C3 ⋊ C4
HallC3×C169⋊C3 ⋊ C4×C5
HallC5×C169 ⋊ C3×Dic3
SylowC169 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(#10621721⋊C3)
commutator, hypocenterC3×C169C3×C4×C5
FrattiniC13C5×C3⋊AGL(1,𝔽13)
FittingC3×C5×C169C3×C4
socleC3×C5×C13AGL(1,𝔽13)
prime radicalC3×C5×D169⋊C3C2
cosocleC3×D169C2×C3×C5
LCSG ▷ C3×C169
UCSC1 ◁ C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2535

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 81);