Finite Group Databasebeta

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Dic3×C29×C13⋊C3 #28330901

order13572
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C29×C13⋊C3
unambiguous semidirect productC3⋊(C4×C29×C13⋊C3)
unambiguous semidirect product(Dic3×C13)⋊(C3×C29)
unambiguous semidirect product(Dic3×C13×C29)⋊C3

Splittings

derivedC3×C13 ⋊ C3×C4×C29
HallC3×C29×C13⋊C3 ⋊ C4
HallC13×C29 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C29
SylowC13 ⋊ C3×Dic3×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29D3×C13⋊C3
commutator, hypocenterC3×C13C3×C4×C29
FrattiniC2D3×C29×C13⋊C3
Fitting, socleC2×C3×C13×C29C2×C3
prime radicalC2×C3×C29×C13⋊C3C2
cosocleC2×C3×C13C2×C3×C29
LCSG ▷ C3×C13
UCSC1 ◁ C2×C29

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4524

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 59);