Finite Group Databasebeta

← Prev (#44568580) Next (#44568582) →

C2×AGL(1,𝔽11)×#3862 #44568581

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×AGL(1,𝔽11)×#3862
unambiguous semidirect productD11⋊(C2×C5×#3862)
unambiguous semidirect product(C2×D11)⋊(C5×#3862)
unambiguous semidirect product(C11⋊C5)⋊(C22×#3862)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×#3862)
unambiguous semidirect product(C2×D11×#3862)⋊C5

Splittings

Fitting, socleC2×C72×C11 ⋊ C2×C3×C5
derived, HallC72×C11 ⋊ C22×C3×C5
HallC2×C72×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×#3862 ⋊ C22
HallC2×D11×#3862 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC2×C72×D11 ⋊ C3×C5
HallC11×#3862 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×#3862
SylowC72 ⋊ C2×C3×AGL(1,𝔽11)
HallC2×D11 ⋊ C5×#3862
SylowC11 ⋊ C22×C5×#3862

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽11)×#3862
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2

200 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 283);