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C11×C37×C22⋊ΓL(1,𝔽8) #46803295

order34188
automorphism?
homologyAbelianization (H1) = C3×C11×C37 · Schur multiplier (H2) = C2

Aliases

direct productC11×C37×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C11×ΓL(1,𝔽8)×C37)
unambiguous semidirect productC7⋊(C11×A4×C37)
unambiguous semidirect product(C22×C11)⋊(ΓL(1,𝔽8)×C37)
unambiguous semidirect product(C7×C11)⋊(A4×C37)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC11×C37C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C11×C37
FrattiniC1G
Fitting, socleC22×C7×C11×C37C3
LCSG ▷ C22×C7
UCSC1 ◁ C11×C37

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

4884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 167);