Finite Group Databasebeta

← Prev (#44568685) Next (#44568687) →

C7×D11×C5⋊AGL(1,𝔽7) #44568686

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D11×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C5×D11)⋊(C7×AGL(1,𝔽7))
unambiguous semidirect product(ΓL(1,𝔽8)×D11)⋊(C7×D5)
unambiguous semidirect product(D11×D35)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C22×C3
derivedC5×C7×C11 ⋊ C22×C3×C7
HallC7×D11×D35 ⋊ C3
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×D11
HallC72×C11 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D11
HallC7×ΓL(1,𝔽8) ⋊ D5×D11
HallC5×C11 ⋊ C2×C7×AGL(1,𝔽7)
SylowC72 ⋊ C3×D5×D11
SylowC11 ⋊ C2×C7×C5⋊AGL(1,𝔽7)
SylowC5 ⋊ C7×D11×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC7D11×C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7×C11C22×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C11C22×C3
LCSG ▷ C5×C7×C11
UCSC1 ◁ C7

168 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 52 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 388);