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C2×C5×C11×D19⋊C3 #27160040

order12540
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D19⋊C3
unambiguous semidirect productD19⋊(C2×C3×C5×C11)
unambiguous semidirect product(C19⋊C3)⋊(C22×C5×C11)
unambiguous semidirect product(C2×D19)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C2×C5×D19)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×D19)⋊C3

Splittings

Fitting, socleC2×C5×C11×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C3×C5×C11
HallC2×C5×C11×D19 ⋊ C3
HallC5×C11×C19⋊C3 ⋊ C22
HallC5×C11×C19 ⋊ C22×C3
HallC2×C11×D19 ⋊ C3×C5
HallC11×C19⋊C3 ⋊ C22×C5
HallC2×C5×D19 ⋊ C3×C11
HallC5×C19⋊C3 ⋊ C22×C11
HallC11×C19 ⋊ C22×C3×C5
HallC5×C19 ⋊ C22×C3×C11
HallC2×D19 ⋊ C3×C5×C11
HallC19⋊C3 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D19⋊C3
commutator, cosocle, hypocenterC19C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

990 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C11×AGL(1,𝔽19), C5×D3×C11×D19⋊C3, C2×C3×C5×C11×D19⋊C3, …
maximal normal subgroup ofC2×C5×C11×AGL(1,𝔽19), C2×C3×C5×C11×D19⋊C3
maximal quotient ofC2×C5×C11×#4294⋊C2, C5×D3×C11×D19⋊C3, C2×C3×C5×C11×D19⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 70);