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C2×(C11⋊C5)⋊#64423 #44568577

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

Aliases

direct productC2×(C11⋊C5)⋊#64423
unambiguous semidirect product(C2×C11⋊C5)⋊#64423
unambiguous semidirect product(C2×C11⋊#64423)⋊C5

Splittings

Fitting, socleC2×C72×C11 ⋊ C2×C3×C5
derived, HallC72×C11 ⋊ C22×C3×C5
HallC2×C7×C7⋊AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×#3861 ⋊ C22
HallC2×C11⋊#64423 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC2×C7×D77 ⋊ 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, hypercenterC2(C11⋊C5)⋊#64423
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2

208 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 308

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 279);