Finite Group Databasebeta

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AGL(1,𝔽7)×D429 #49114733

order36036
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽7)×D429
unambiguous semidirect productD7⋊(C3×D429)
unambiguous semidirect product(C3×AGL(1,𝔽7))⋊D143
unambiguous semidirect product(C11×AGL(1,𝔽7))⋊D39
unambiguous semidirect product(C13×AGL(1,𝔽7))⋊D33

Splittings

Fitting, socle, derivedC3×C7×C11×C13 ⋊ C22×C3
HallC3×C11×C13×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×C13 ⋊ C2×C3×D3
HallC3×C13×ΓL(1,𝔽8) ⋊ C2×D11
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×D13
HallC11×C13 ⋊ D3×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D33
HallC7×C11 ⋊ C2×C3×D39
HallC3×ΓL(1,𝔽8) ⋊ C2×D143
SylowC13 ⋊ AGL(1,𝔽7)×D33
SylowC11 ⋊ AGL(1,𝔽7)×D39
SylowC7 ⋊ C2×C3×D429

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 401);