Finite Group Databasebeta

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C3×C4×C53×C19⋊C3 #49136254

order36252
automorphism?
homologyAbelianization (H1) = C32×C4×C53 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C53×C19⋊C3
unambiguous semidirect product(C4×C19)⋊(C32×C53)
unambiguous semidirect product(C3×C4×C19)⋊(C3×C53)
unambiguous semidirect product(C4×C19×C53)⋊C32
unambiguous semidirect product(C3×C4×C19×C53)⋊C3

Splittings

FittingC3×C4×C19×C53 ⋊ C3
derived, SylowC19 ⋊ C32×C4×C53
HallC4×C19×C53 ⋊ C32
HallC19×C53 ⋊ C32×C4
HallC4×C19 ⋊ C32×C53

Subgroups

subgroupG/H
center, hypercenterC3×C4×C53C19⋊C3
commutator, hypocenterC19C32×C4×C53
FrattiniC2C2×C3×C53×C19⋊C3
FittingC3×C4×C19×C53C3
socleC2×C3×C19×C53C2×C3
prime radicalC2×C3×C53×C19⋊C3C2
cosocleC2×C19C2×C32×C53
LCSG ▷ C19
UCSC1 ◁ C3×C4×C53

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12084

Conjugacy classes & character table

5724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 53);