Finite Group Databasebeta

← Prev (#44501808) Next (#44501810) →

C3×D3×C31×C11⋊C5 #44501809

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3×C31×C11⋊C5
unambiguous semidirect productC3⋊(C2×C3×C31×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C3×C5×C31)
unambiguous semidirect product(C3×D3×C11)⋊(C5×C31)

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derivedC3×C11 ⋊ C2×C3×C5×C31
HallC32×C31×C11⋊C5 ⋊ C2
HallC3×D3×C11×C31 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ C2×C11⋊C5
HallC3×D3×C11 ⋊ C5×C31
HallC32×C11 ⋊ C2×C5×C31
SylowC11 ⋊ C3×C5×D3×C31
SylowC32 ⋊ C2×C31×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C31D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C3×C5×C31
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C3×C31

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2046

Conjugacy classes & character table

1953 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 176);