Finite Group Databasebeta

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AGL(1,𝔽11)×#64418 #44568540

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

Aliases

direct productAGL(1,𝔽11)×#64418
unambiguous semidirect productD11⋊(C5×#64418)
unambiguous semidirect product(D11×#64418)⋊C5

Splittings

Fitting, socle, HallC72×C11 ⋊ C2×C5×D3
derived, HallC11×#3862 ⋊ C22×C5
HallC11⋊C5×#3862 ⋊ C22
HallD11×#64418 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×D3
Hall#3862 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×#64418
SylowC72 ⋊ D3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×#64418

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC11×#3862C22×C5
Fitting, socleC72×C11C2×C5×D3
LCSG ▷ C11×#3862
UCSC1

136 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 22 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) = 154

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 242);