Finite Group Databasebeta

← Prev (#49179996) Next (#49179998) →

C29×(C31⋊C3)⋊D7 #49179997

order37758
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×(C31⋊C3)⋊D7
unambiguous semidirect product(C31⋊C3)⋊(D7×C29)

Splittings

Fitting, socle, HallC7×C29×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C3×C29
HallC7×C29×C31⋊C3 ⋊ C2
HallC29×D217 ⋊ C3
HallC29×C31⋊C3 ⋊ D7
HallC29×C31 ⋊ C3×D7
HallC7×C31⋊C3 ⋊ C2×C29
HallD217 ⋊ C3×C29
HallC7×C29 ⋊ D31⋊C3
HallC31⋊C3 ⋊ D7×C29
SylowC31 ⋊ C3×D7×C29
SylowC7 ⋊ C29×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC29(C31⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C31C2×C3×C29
FrattiniC1G
Fitting, socleC7×C29×C31C2×C3
LCSG ▷ C7×C31
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6293

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37758, 46);