Finite Group Databasebeta

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C2×C3×C53×D19⋊C3 #49136287

order36252
automorphism?
homologyAbelianization (H1) = C22×C32×C53 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C53×D19⋊C3
unambiguous semidirect productD19⋊(C2×C32×C53)
unambiguous semidirect product(C19⋊C3)⋊(C22×C3×C53)
unambiguous semidirect product(C2×D19)⋊(C32×C53)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C3×C53)
unambiguous semidirect product(C2×C3×D19)⋊(C3×C53)
unambiguous semidirect product(C2×D19×C53)⋊C32
unambiguous semidirect product(C2×C3×D19×C53)⋊C3

Splittings

Fitting, socleC2×C3×C19×C53 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C32×C53
HallC3×C53×C19⋊C3 ⋊ C22
HallC2×D19×C53 ⋊ C32
HallC19×C53 ⋊ C22×C32
HallC3×C19⋊C3 ⋊ C22×C53
HallC2×D19 ⋊ C32×C53

Subgroups

subgroupG/H
center, hypercenterC2×C3×C53D19⋊C3
commutator, cosocle, hypocenterC19C22×C32×C53
FrattiniC1G
Fitting, socleC2×C3×C19×C53C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C3×C53

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6042

Conjugacy classes & character table

2862 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 86);