Finite Group Databasebeta

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C2×C11⋊C5×D141 #44526637

order31020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊C5×D141
unambiguous semidirect product(C2×C3)⋊(C11⋊C5×D47)
unambiguous semidirect product(C2×C47)⋊(D3×C11⋊C5)
unambiguous semidirect product(C2×C11×D141)⋊C5

Splittings

Fitting, socleC2×C3×C11×C47 ⋊ C2×C5
derived, HallC3×C11×C47 ⋊ C22×C5
HallC3×C47×C11⋊C5 ⋊ C22
HallC2×C11×D141 ⋊ C5
HallC47×C11⋊C5 ⋊ C2×D3
HallC11×C47 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D47
HallC3×C47 ⋊ C22×C11⋊C5
SylowC47 ⋊ C2×D3×C11⋊C5
HallC3×C11 ⋊ C2×C5×D47
SylowC11 ⋊ C2×C5×D141
SylowC3 ⋊ C2×C11⋊C5×D47

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D141
commutator, cosocle, hypocenterC3×C11×C47C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C47C2×C5
LCSG ▷ C3×C11×C47
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3102

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 40);