Finite Group Databasebeta

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C29×C3⋊(Dic13⋊C3) #28330899

order13572
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C29×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C29)
unambiguous semidirect product(C29×Dic39)⋊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×C29C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C29
FrattiniC2C29×C3⋊(D13⋊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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 57);