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D11×C5⋊(D49⋊C3) #44568355

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

Aliases

direct productD11×C5⋊(D49⋊C3)
unambiguous semidirect product(C5×D11)⋊(D49⋊C3)
unambiguous semidirect product(D11×C49⋊C3)⋊D5
unambiguous semidirect product(D11×D245)⋊C3

Splittings

Fitting, derived, HallC5×C11×C49 ⋊ C22×C3
HallD11×D245 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C22
HallC11×C49⋊C3 ⋊ C2×D5
HallC5×C49⋊C3 ⋊ C2×D11
HallC11×C49 ⋊ C2×C3×D5
HallC5×C49 ⋊ C2×C3×D11
HallC49⋊C3 ⋊ D5×D11
HallC5×C11 ⋊ C2×D49⋊C3
SylowC49 ⋊ C3×D5×D11
SylowC11 ⋊ C2×C5⋊(D49⋊C3)
SylowC5 ⋊ D11×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C11×C49C22×C3
FrattiniC7D11×C5⋊AGL(1,𝔽7)
socleC5×C7×C11C2×AGL(1,𝔽7)
LCSG ▷ C5×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 57);