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C₉×D₁₉×D₅₃ #49136223

order	36252
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₉×D₅₃

Splittings

Fitting, Hall	C₉×C₁₉×C₅₃ ⋊ C₂²
derived, Hall	C₁₉×C₅₃ ⋊ C₂²×C₉
Hall	C₉×C₅₃ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₅₃
Sylow	C₅₃ ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×D₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₉×D₅₃
commutator, hypocenter	C₁₉×C₅₃	C₂²×C₉
Frattini	C₃	C₃×D₁₉×D₅₃
Fitting	C₉×C₁₉×C₅₃	C₂²
socle, cosocle	C₃×C₁₉×C₅₃	C₂²×C₃
prime radical	C₃×D₁₉×D₅₃	C₃
LCS	G ▷ C₁₉×C₅₃
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9063

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 22);