Finite Group Databasebeta

← Prev (#37552891) Next (#37552893) →

D3×C11×C71⋊C5 #37552892

order23430
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11×C71⋊C5
unambiguous semidirect productC3⋊(C2×C11×C71⋊C5)
unambiguous semidirect product(D3×C71)⋊(C5×C11)

Splittings

Fitting, socle, HallC3×C11×C71 ⋊ C2×C5
derived, HallC3×C71 ⋊ C2×C5×C11
HallC3×C11×C71⋊C5 ⋊ C2
HallD3×C11×C71 ⋊ C5
HallC3×C71⋊C5 ⋊ C2×C11
HallC11×C71 ⋊ C5×D3
HallD3×C71 ⋊ C5×C11
SylowC71 ⋊ C5×D3×C11
HallC3×C11 ⋊ C2×C71⋊C5
SylowC3 ⋊ C2×C11×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC11D3×C71⋊C5
commutator, cosocle, hypocenterC3×C71C2×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C71C2×C5
LCSG ▷ C3×C71
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 41);