Finite Group Databasebeta

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C3×C37⋊C3×Dic29 #50311173

order38628
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C37⋊C3×Dic29
unambiguous semidirect product(C37×Dic29)⋊C32
unambiguous semidirect product(C3×C37×Dic29)⋊C3

Splittings

derived, HallC29×C37 ⋊ C32×C4
HallC3×C29×C37⋊C3 ⋊ C4
HallC37×Dic29 ⋊ C32
SylowC37 ⋊ C32×Dic29
SylowC29 ⋊ C3×C4×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D29×C37⋊C3
commutator, hypocenterC29×C37C32×C4
FrattiniC2C3×D29×C37⋊C3
Fitting, socleC2×C3×C29×C37C2×C3
prime radicalC2×C3×C29×C37⋊C3C2
cosocleC2×C29×C37C2×C32
LCSG ▷ C29×C37
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12876

Conjugacy classes & character table

1440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38628, 60);