Finite Group Databasebeta

← Prev (#41004203) Next (#41004205) →

D3×C29×ΓL(1,𝔽32) #41004204

order26970
automorphism?
homologyAbelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productD3×C29×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C2×C29×ΓL(1,𝔽32))
unambiguous semidirect product(D3×C31)⋊(C5×C29)
unambiguous semidirect product(D3×C29×C31)⋊C5

Splittings

Fitting, socle, HallC3×C29×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C2×C5×C29
HallC3×C29×ΓL(1,𝔽32) ⋊ C2
HallD3×C29×C31 ⋊ C5
HallC29×C31 ⋊ C5×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×C29
HallD3×C31 ⋊ C5×C29
HallC3×C29 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D3×C29
SylowC3 ⋊ C2×C29×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC29D3×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC3×C31C2×C5×C29
FrattiniC1G
Fitting, socleC3×C29×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 23);