Finite Group Databasebeta

← Prev (#44526686) Next (#44526688) →

C2×C3×C11×D235 #44526687

order31020
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D235
unambiguous semidirect product(C2×C5)⋊(C3×C11×D47)
unambiguous semidirect product(C2×C47)⋊(C3×D5×C11)

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC5×C47 ⋊ C22×C3×C11
HallC3×C5×C11×C47 ⋊ C22
HallC5×C11×C47 ⋊ C22×C3
HallC3×C11×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C22×C11
HallC11×C47 ⋊ C2×C3×D5
HallC3×C5×C11 ⋊ C2×D47
HallC3×C47 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C3×D47
SylowC47 ⋊ C2×C3×D5×C11
HallC3×C5 ⋊ C2×C11×D47
SylowC5 ⋊ C2×C3×C11×D47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D235
commutator, cosocle, hypocenterC5×C47C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C5×C47
UCSC1 ◁ C2×C3×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15510

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 90);