Finite Group Databasebeta

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Dic₃×C₅₃×C₁₉⋊C₃ #49136252

order	36252
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₅₃×C₁₉⋊C₃
unambiguous semidirect product	C₃⋊(C₄×C₅₃×C₁₉⋊C₃)
unambiguous semidirect product	(Dic₃×C₁₉)⋊(C₃×C₅₃)
unambiguous semidirect product	(Dic₃×C₁₉×C₅₃)⋊C₃

Splittings

derived	C₃×C₁₉ ⋊ C₃×C₄×C₅₃
Hall	C₃×C₅₃×C₁₉⋊C₃ ⋊ C₄
Hall	C₁₉×C₅₃ ⋊ C₃×Dic₃
Hall	C₃×C₁₉⋊C₃ ⋊ C₄×C₅₃
Sylow	C₁₉ ⋊ C₃×Dic₃×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅₃	D₃×C₁₉⋊C₃
commutator, hypocenter	C₃×C₁₉	C₃×C₄×C₅₃
Frattini	C₂	D₃×C₅₃×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₂×C₃×C₅₃×C₁₉⋊C₃	C₂
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₅₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₅₃

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12084

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, 51);