Finite Group Databasebeta

← Prev (#44568627) Next (#44568629) →

C5×C11×D7×AGL(1,𝔽7) #44568628

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×D7×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C5×C11×D7)
unambiguous semidirect product(C7×AGL(1,𝔽7))⋊(C2×C5×C11)
unambiguous semidirect product(D7×ΓL(1,𝔽8))⋊(C2×C5×C11)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D7)⋊(C2×C5×C11)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C22×C3
derived, SylowC72 ⋊ C22×C3×C5×C11
HallC5×C11×D72 ⋊ C3
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C22
HallC11×D72 ⋊ C3×C5
HallC7×C11×ΓL(1,𝔽8) ⋊ C22×C5
HallC5×D72 ⋊ C3×C11
HallC5×C7×ΓL(1,𝔽8) ⋊ C22×C11
HallC72×C11 ⋊ C22×C3×C5
HallC5×C72 ⋊ C22×C3×C11
HallD72 ⋊ C3×C5×C11
HallC7×ΓL(1,𝔽8) ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D7×AGL(1,𝔽7)
commutator, cosocle, hypocenterC72C22×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C22×C3
LCSG ▷ C72
UCSC1 ◁ C5×C11

168 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 2310

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 330);