Finite Group Databasebeta

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C3×C4×C5×C169⋊C3 #44477472

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C5×C169⋊C3
unambiguous semidirect product(C4×C169)⋊(C32×C5)
unambiguous semidirect product(C3×C4×C169)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C169)⋊C32
unambiguous semidirect product(C3×C4×C5×C169)⋊C3

Splittings

FittingC3×C4×C5×C169 ⋊ C3
derived, SylowC169 ⋊ C32×C4×C5
HallC4×C5×C169 ⋊ C32
HallC5×C169 ⋊ C32×C4
HallC4×C169 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C169⋊C3
commutator, hypocenterC169C32×C4×C5
FrattiniC2×C13C2×C3×C5×C13⋊C3
FittingC3×C4×C5×C169C3
socleC2×C3×C5×C13C2×C13⋊C3
prime radicalC2×C3×C5×C169⋊C3C2
cosocleC2×C169C2×C32×C5
LCSG ▷ C169
UCSC1 ◁ C3×C4×C5

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10140

Conjugacy classes & character table

3540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 61);