Finite Group Databasebeta

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C2×C11⋊#13095537 #46803232

order34188
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊#13095537
unambiguous semidirect product(C2×C11)⋊#13095537

Splittings

Fitting, socleC2×C7×C11×C37 ⋊ C2×C3
derived, HallC7×C11×C37 ⋊ C22×C3
HallC2×D2849 ⋊ C3
HallC11×#11715913 ⋊ C22
Hall#11715913 ⋊ C2×D11
HallC11×C37 ⋊ C2×AGL(1,𝔽7)
HallC7×C37 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D37⋊C3
SylowC37 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×#13095537
SylowC7 ⋊ C2×C11⋊(D37⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C11⋊#13095537
commutator, cosocle, hypocenterC7×C11×C37C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C37C2×C3
LCSG ▷ C7×C11×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5698

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 104);