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D55×D19⋊C3 #27160028

order12540
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD55×D19⋊C3
unambiguous semidirect productD19⋊(C3×D55)
unambiguous semidirect product(C5×D19⋊C3)⋊D11
unambiguous semidirect product(C11×D19⋊C3)⋊D5
unambiguous semidirect product(D19×D55)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C19 ⋊ C22×C3
HallD19×D55 ⋊ C3
HallC5×C11×C19⋊C3 ⋊ C22
HallC11×C19⋊C3 ⋊ C2×D5
HallC5×C19⋊C3 ⋊ C2×D11
HallC11×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×C3×D11
HallC19⋊C3 ⋊ C2×D55
HallC5×C11 ⋊ C2×D19⋊C3
SylowC19 ⋊ C2×C3×D55
SylowC11 ⋊ D5×D19⋊C3
SylowC5 ⋊ D11×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C19C22×C3
LCSG ▷ C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

261 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD55×AGL(1,𝔽19), C3×D55×D19⋊C3, D19⋊C3×D165, …
maximal normal subgroup ofD55×AGL(1,𝔽19), C3×D55×D19⋊C3
maximal quotient ofD55×#4294⋊C2, C3×D55×D19⋊C3, D19⋊C3×D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 58);