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AGL(1,𝔽7)×D407 #46803197

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

Aliases

direct productAGL(1,𝔽7)×D407
unambiguous semidirect productD7⋊(C3×D407)
unambiguous semidirect product(C11×AGL(1,𝔽7))⋊D37
unambiguous semidirect product(C37×AGL(1,𝔽7))⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C37 ⋊ C22×C3
HallD7×D407 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C22
HallΓL(1,𝔽8)×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×AGL(1,𝔽7)
HallC7×C37 ⋊ C2×C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D37
HallC7×C11 ⋊ C2×C3×D37
SylowC37 ⋊ D11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×D407
SylowC11 ⋊ AGL(1,𝔽7)×D37
SylowC7 ⋊ C2×C3×D407

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C37C22×C3
LCSG ▷ C7×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2849

Conjugacy classes & character table

1435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 69);