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C₁₉×Dic₉×C₅₃ #49136207

order	36252
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₉×C₅₃
unambiguous semidirect product	C₉⋊(C₄×C₁₉×C₅₃)

Splittings

derived, Sylow	C₉ ⋊ C₄×C₁₉×C₅₃
Hall	C₉×C₁₉×C₅₃ ⋊ C₄
Hall	C₉×C₅₃ ⋊ C₄×C₁₉
Hall	C₉×C₁₉ ⋊ C₄×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₅₃	D₉
commutator, hypocenter	C₉	C₄×C₁₉×C₅₃
Frattini	C₂×C₃	D₃×C₁₉×C₅₃
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle, prime radical	C₂×C₃×C₁₉×C₅₃	D₃
cosocle	C₂×C₉	C₂×C₁₉×C₅₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₅₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 36252

Conjugacy classes & character table

12084 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 6);