Finite Group Databasebeta

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C11×C22⋊#11715913 #46803296

order34188
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊#11715913
unambiguous semidirect productC22⋊(C11×#11715913)
unambiguous semidirect product(C22×C11)⋊#11715913

Splittings

Fitting, socle, HallC22×C7×C11×C37 ⋊ C3
derived, HallC22×C7×C37 ⋊ C3×C11
HallC7×C11×C37 ⋊ A4
HallC22×C11×C37 ⋊ ΓL(1,𝔽8)
HallC11×C37 ⋊ C22⋊ΓL(1,𝔽8)
HallC22×C7×C11 ⋊ C37⋊C3
HallC7×C37 ⋊ C11×A4
HallC22×C37 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C22⋊(C37⋊C3)
HallC22×C11 ⋊ #11715913
SylowC37 ⋊ C11×C22⋊ΓL(1,𝔽8)
HallC22×C7 ⋊ C11×C37⋊C3
SylowC7 ⋊ C11×C22⋊(C37⋊C3)
SylowC22 ⋊ C11×#11715913

Subgroups

subgroupG/H
center, hypercenterC11C22⋊#11715913
commutator, cosocle, hypocenterC22×C7×C37C3×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C37C3
LCSG ▷ C22×C7×C37
UCSC1 ◁ C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

3828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 168);