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AGL(1,𝔽11)×#64423 #44568556

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

Aliases

direct productAGL(1,𝔽11)×#64423
unambiguous semidirect productD11⋊(C5×#64423)
unambiguous semidirect product(D11×#64423)⋊C5

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C22×C3×C5
HallC7×D7×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×#3861 ⋊ C22
HallD11×#64423 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC7×D7×D11 ⋊ C3×C5
HallC11×#3861 ⋊ C22×C5
Hall#3861 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×#64423
SylowC72 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×#64423

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C22×C3×C5
LCSG ▷ C72×C11
UCSC1

208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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

187 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#64423⋊C2
maximal normal subgroup ofAGL(1,𝔽11)×#64423⋊C2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 258);