Finite Group Databasebeta

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D3×C31×C29⋊C7 #49179977

order37758
automorphism?
homologyAbelianization (H1) = C2×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productD3×C31×C29⋊C7
unambiguous semidirect productC3⋊(C2×C31×C29⋊C7)
unambiguous semidirect product(D3×C29)⋊(C7×C31)
unambiguous semidirect product(D3×C29×C31)⋊C7

Splittings

Fitting, socle, HallC3×C29×C31 ⋊ C2×C7
derived, HallC3×C29 ⋊ C2×C7×C31
HallC3×C31×C29⋊C7 ⋊ C2
HallD3×C29×C31 ⋊ C7
HallC29×C31 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C2×C31
HallD3×C29 ⋊ C7×C31
HallC3×C31 ⋊ C2×C29⋊C7
SylowC29 ⋊ D3×C7×C31
SylowC3 ⋊ C2×C31×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC31D3×C29⋊C7
commutator, cosocle, hypocenterC3×C29C2×C7×C31
FrattiniC1G
Fitting, socleC3×C29×C31C2×C7
LCSG ▷ C3×C29
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

1023 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37758, 26);