Finite Group Databasebeta

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C2×D11×#11715913 #46803243

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

Aliases

direct productC2×D11×#11715913
unambiguous semidirect productC11⋊(C22×#11715913)
unambiguous semidirect product(C2×C11)⋊(C2×#11715913)

Splittings

Fitting, socleC2×C7×C11×C37 ⋊ C2×C3
derived, HallC7×C11×C37 ⋊ C22×C3
HallC2×C7×D11×C37 ⋊ C3
HallC11×#11715913 ⋊ C22
HallC2×D11×C37 ⋊ ΓL(1,𝔽8)
HallC11×C37 ⋊ C22×ΓL(1,𝔽8)
HallC2×C7×D11 ⋊ C37⋊C3
HallC7×C37 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C37⋊C3
SylowC37 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C22×#11715913
SylowC7 ⋊ C2×D11×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D11×#11715913
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

1246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 115);