Finite Group Databasebeta

← Prev (#44545543) Next (#44545545) →

C3×C23×(C31⋊C3)⋊C5 #44545544

order32085
automorphism?
homologyAbelianization (H1) = C32×C5×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C3×C5×C23)
unambiguous semidirect productΓL(1,𝔽32)⋊(C32×C23)
unambiguous semidirect product(C3×C31⋊C3)⋊(C5×C23)
unambiguous semidirect product(C3×ΓL(1,𝔽32))⋊(C3×C23)
unambiguous semidirect product(C23×C31⋊C3)⋊(C3×C5)
unambiguous semidirect product(C23×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C3×C23×C31⋊C3)⋊C5
unambiguous semidirect product(C3×C23×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC3×C23×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C32×C5×C23
HallC3×C23×C31⋊C3 ⋊ C5
HallC23×ΓL(1,𝔽32) ⋊ C32
HallC23×C31 ⋊ C32×C5
HallC3×C31⋊C3 ⋊ C5×C23
HallΓL(1,𝔽32) ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC3×C23(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C32×C5×C23
FrattiniC1G
Fitting, socleC3×C23×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2139

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32085, 6);