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C3×D55⋊D19 #27160058

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

Aliases

direct productC3×D55⋊D19
unambiguous semidirect productD55⋊(C3×D19)

Splittings

Fitting, socle, HallC3×C5×C11×C19 ⋊ C22
derived, HallC5×C11×C19 ⋊ C22×C3
HallC3×C11×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D11
HallC11×C19 ⋊ C2×C3×D5
HallC3×C5×C11 ⋊ C2×D19
HallC5×C19 ⋊ C2×C3×D11
HallC3×C19 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3×D19
HallC3×C11 ⋊ D5×D19
SylowC19 ⋊ C3×D5×D11
HallC3×C5 ⋊ D11×D19
SylowC11 ⋊ C3×D5×D19
SylowC5 ⋊ C3×D11×D19

Subgroups

subgroupG/H
center, hypercenterC3D55⋊D19
commutator, cosocle, hypocenterC5×C11×C19C22×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C19C22
LCSG ▷ C5×C11×C19
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

867 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD55⋊(#4294⋊C2), C9×D55⋊D19, C3×D55⋊(D19⋊C3), …
maximal normal subgroup ofD55⋊(#4294⋊C2), C9×D55⋊D19, C3×D55⋊(D19⋊C3), …
maximal quotient ofC9×D55⋊D19, C32×D55⋊D19, C3×D209⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 88);