Finite Group Databasebeta

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C2×C11×D705 #44526695

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

Aliases

direct productC2×C11×D705
unambiguous semidirect product(C2×C3)⋊(C11×D235)
unambiguous semidirect product(C2×C5)⋊(C11×D141)
unambiguous semidirect product(C2×C47)⋊(C11×D15)

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC3×C5×C47 ⋊ C22×C11
HallC3×C5×C11×C47 ⋊ C22
HallC5×C11×C47 ⋊ C2×D3
HallC3×C11×C47 ⋊ C2×D5
HallC11×C47 ⋊ C2×D15
HallC5×C47 ⋊ C2×D3×C11
HallC3×C5×C11 ⋊ C2×D47
HallC3×C47 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×D141
SylowC47 ⋊ C2×C11×D15
HallC3×C11 ⋊ C2×D235
HallC3×C5 ⋊ C2×C11×D47
SylowC5 ⋊ C2×C11×D141
SylowC3 ⋊ C2×C11×D235

Subgroups

subgroupG/H
center, hypercenterC2×C11D705
commutator, cosocle, hypocenterC3×C5×C47C22×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C3×C5×C47
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15510

Conjugacy classes & character table

7788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 98);