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C11×AGL(1,𝔽7)×D37 #46803186

order34188
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×AGL(1,𝔽7)×D37
unambiguous semidirect productD7⋊(C3×C11×D37)
unambiguous semidirect product(ΓL(1,𝔽8)×D37)⋊(C2×C11)
unambiguous semidirect product(C37×AGL(1,𝔽7))⋊(C2×C11)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D37)⋊(C2×C11)

Splittings

Fitting, socle, HallC7×C11×C37 ⋊ C22×C3
derived, HallC7×C37 ⋊ C22×C3×C11
HallC11×D7×D37 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C22
HallD7×D37 ⋊ C3×C11
HallΓL(1,𝔽8)×C37 ⋊ C22×C11
HallC11×C37 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C2×D37
HallC7×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C2×C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C11×D37
SylowC7 ⋊ C2×C3×C11×D37

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽7)×D37
commutator, cosocle, hypocenterC7×C37C22×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C37C22×C3
LCSG ▷ C7×C37
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2849

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 58);