Finite Group Databasebeta

← Prev (#49136240) Next (#49136242) →

C₂×C₉×C₁₉×D₅₃ #49136241

order	36252
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×C₁₉×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂²×C₉×C₁₉)
unambiguous semidirect product	(C₂×C₅₃)⋊(C₂×C₉×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₅₃
commutator, hypocenter	C₅₃	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×D₅₃
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₂×C₃×C₁₉×D₅₃	C₃
cosocle	C₃×C₅₃	C₂²×C₃×C₁₉
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₉×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18126

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, 40);