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C3×(C7⋊D7)⋊AGL(1,𝔽11) #44568588

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

Aliases

direct productC3×(C7⋊D7)⋊AGL(1,𝔽11)
unambiguous semidirect product(C3×(C7⋊D7)⋊D11)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C22×C5
derived, HallC72×C11 ⋊ C22×C3×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallC3×(C7⋊D7)⋊D11 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
Hall(C7⋊D7)⋊D11 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ D72
HallC3×C72 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D72
SylowC72 ⋊ C2×C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D72
SylowC11 ⋊ C3×C5×D72

Subgroups

subgroupG/H
center, hypercenterC3(C7⋊D7)⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C72×C11C22×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 290);