Finite Group Databasebeta

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C₉×C₁₉×Dic₅₃ #49136204

order	36252
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×Dic₅₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₅₃
commutator, hypocenter	C₅₃	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×C₁₉×D₅₃
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle, prime radical	C₂×C₃×C₁₉×C₅₃	C₂×C₃
cosocle	C₂×C₃×C₅₃	C₂×C₃×C₁₉
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₉×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 36252

Conjugacy classes & character table

9576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 3);