Finite Group Databasebeta

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C3×C31⋊(D29⋊C7) #49179976

order37758
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31⋊(D29⋊C7)
unambiguous semidirect product(C29⋊C7)⋊(C3×D31)
unambiguous semidirect product(C3×D899)⋊C7

Splittings

Fitting, socle, HallC3×C29×C31 ⋊ C2×C7
derived, HallC29×C31 ⋊ C2×C3×C7
HallC3×C31×C29⋊C7 ⋊ C2
HallC31×C29⋊C7 ⋊ C2×C3
HallC3×D899 ⋊ C7
HallD899 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ D31
HallC29⋊C7 ⋊ C3×D31
HallC3×C31 ⋊ D29⋊C7
HallC3×C29 ⋊ C7×D31
SylowC31 ⋊ C3×D29⋊C7
SylowC29 ⋊ C3×C7×D31

Subgroups

subgroupG/H
center, hypercenterC3C31⋊(D29⋊C7)
commutator, cosocle, hypocenterC29×C31C2×C3×C7
FrattiniC1G
Fitting, socleC3×C29×C31C2×C7
LCSG ▷ C29×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37758, 25);