Finite Group Databasebeta

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C29×C3⋊(Dic37⋊C3) #50311174

order38628
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C3⋊(Dic37⋊C3)
unambiguous semidirect productC3⋊(C29×Dic37⋊C3)
unambiguous semidirect productDic111⋊(C3×C29)
unambiguous semidirect product(C29×Dic111)⋊C3

Splittings

derivedC3×C37 ⋊ C3×C4×C29
HallC3×C29×C37⋊C3 ⋊ C4
HallC29×C37 ⋊ C3×Dic3
HallC3×C37⋊C3 ⋊ C4×C29
SylowC37 ⋊ C3×Dic3×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29C3⋊(D37⋊C3)
commutator, hypocenterC3×C37C3×C4×C29
FrattiniC2C29×C3⋊(D37⋊C3)
Fitting, socleC2×C3×C29×C37C2×C3
prime radicalC2×C3×C29×C37⋊C3C2
cosocleC2×C3×C37C2×C3×C29
LCSG ▷ C3×C37
UCSC1 ◁ C2×C29

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12876

Conjugacy classes & character table

1566 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 61);