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C₂×C₉×D₁₉×C₅₃ #49136240

order	36252
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₅₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₁₉×C₅₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₅₃	D₁₉
commutator, hypocenter	C₁₉	C₂²×C₉×C₅₃
Frattini	C₃	C₂×C₃×D₁₉×C₅₃
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₂×C₃×D₁₉×C₅₃	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₅₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₅₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18126

Conjugacy classes & character table

10494 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 39);