Finite Group Databasebeta

← Prev (#49088972) Next (#49088974) →

C3×C7×#13133723 #49088973

order35805
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×#13133723

Splittings

Fitting, socle, HallC3×C7×C11×C31 ⋊ C5
derived, HallC11×C31 ⋊ C3×C5×C7
HallC7×C11×C31 ⋊ C3×C5
HallC3×C11×C31 ⋊ C5×C7
HallC3×C7×C31 ⋊ C11⋊C5
HallC3×C7×C11 ⋊ ΓL(1,𝔽32)
HallC7×C31 ⋊ C3×C11⋊C5
HallC3×C31 ⋊ C7×C11⋊C5
HallC7×C11 ⋊ C3×ΓL(1,𝔽32)
HallC3×C11 ⋊ C7×ΓL(1,𝔽32)
SylowC31 ⋊ C3×C7×C11⋊C5
SylowC11 ⋊ C3×C7×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3×C7#13133723
commutator, cosocle, hypocenterC11×C31C3×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C31C5
LCSG ▷ C11×C31
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7161

Conjugacy classes & character table

1533 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35805, 5);