Finite Group Databasebeta

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C2×C37×C11⋊AGL(1,𝔽7) #46803231

order34188
automorphism?
homologyAbelianization (H1) = C22×C3×C37 · Schur multiplier (H2) = C2

Aliases

direct productC2×C37×C11⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C11)⋊(C37×AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D11×C37)
unambiguous semidirect product(C2×D77)⋊(C3×C37)

Splittings

Fitting, socleC2×C7×C11×C37 ⋊ C2×C3
derived, HallC7×C11 ⋊ C22×C3×C37
HallC2×C37×D77 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C22
HallC7×C11×C37 ⋊ C22×C3
HallΓL(1,𝔽8)×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×AGL(1,𝔽7)
HallC2×D77 ⋊ C3×C37
HallC7×C37 ⋊ C2×C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C22×C37
HallΓL(1,𝔽8) ⋊ C2×D11×C37
SylowC11 ⋊ C2×C37×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C37C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C22×C3×C37
FrattiniC1G
Fitting, socleC2×C7×C11×C37C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C2×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5698

Conjugacy classes & character table

2368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 103);