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C₃×C₁₉×Dic₁₅₉ #49136261

order	36252
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×Dic₁₅₉
unambiguous semidirect product	C₃⋊(C₃×C₁₉×Dic₅₃)

Splittings

derived	C₃×C₅₃ ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₁₉×C₅₃ ⋊ C₄
Hall	C₁₉×C₅₃ ⋊ C₃×Dic₃
Hall	C₃²×C₅₃ ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ Dic₅₃
Sylow	C₅₃ ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×Dic₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₅₉
commutator, hypocenter	C₃×C₅₃	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₁₅₉
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₅₃	C₂
cosocle	C₂×C₃×C₅₃	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₅₃
UCS	C₁ ◁ C₂×C₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12084

Conjugacy classes & character table

9234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 60);