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AGL(1,𝔽7)×D377 #44539845

order31668
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽7)×D377
unambiguous semidirect productD7⋊(C3×D377)
unambiguous semidirect product(C13×AGL(1,𝔽7))⋊D29
unambiguous semidirect product(C29×AGL(1,𝔽7))⋊D13

Splittings

Fitting, socle, derived, HallC7×C13×C29 ⋊ C22×C3
HallD7×D377 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C22
HallΓL(1,𝔽8)×C29 ⋊ C2×D13
HallC13×C29 ⋊ C2×AGL(1,𝔽7)
HallC13×ΓL(1,𝔽8) ⋊ C2×D29
HallC7×C29 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×D29
SylowC29 ⋊ D13×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×D377
SylowC13 ⋊ AGL(1,𝔽7)×D29
SylowC7 ⋊ C2×C3×D377

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C29C22×C3
LCSG ▷ C7×C13×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 140);