Finite Group Databasebeta

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C2×C11×C37×AGL(1,𝔽7) #46803225

order34188
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C37 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C37×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C11×C37)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C11×C37)
unambiguous semidirect product(C2×D7)⋊(C3×C11×C37)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C11×C37)
unambiguous semidirect product(C2×C11×D7)⋊(C3×C37)

Splittings

Fitting, socleC2×C7×C11×C37 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C11×C37
HallC2×C11×D7×C37 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C22
HallC7×C11×C37 ⋊ C22×C3
HallC2×D7×C37 ⋊ C3×C11
HallΓL(1,𝔽8)×C37 ⋊ C22×C11
HallC2×C11×D7 ⋊ C3×C37
HallC7×C37 ⋊ C22×C3×C11
HallC11×ΓL(1,𝔽8) ⋊ C22×C37
HallC7×C11 ⋊ C22×C3×C37
HallC2×D7 ⋊ C3×C11×C37
HallΓL(1,𝔽8) ⋊ C22×C11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C11×C37AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C11×C37
FrattiniC1G
Fitting, socleC2×C7×C11×C37C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5698

Conjugacy classes & character table

5698 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 97);