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C₁₉×C₂²⋊(C₃₁⋊C₉) #35234355

order	21204
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×C₂²⋊(C₃₁⋊C₉)
unambiguous semidirect product	C₂²⋊(C₁₉×C₃₁⋊C₉)
unambiguous semidirect product	C₃₁⋊(C₁₉×C₂²⋊C₉)

Splittings

derived, Hall	C₂²×C₃₁ ⋊ C₉×C₁₉
Hall	C₂²×C₁₉×C₃₁ ⋊ C₉
Hall	C₁₉×C₃₁ ⋊ C₂²⋊C₉
Hall	C₂²×C₁₉ ⋊ C₃₁⋊C₉
Sylow	C₃₁ ⋊ C₁₉×C₂²⋊C₉
Sylow	C₂² ⋊ C₁₉×C₃₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₂²⋊(C₃₁⋊C₃)
commutator, hypocenter	C₂²×C₃₁	C₉×C₁₉
Frattini	C₃	C₁₉×C₂²⋊(C₃₁⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₁₉×C₃₁	C₃
cosocle	C₂²×C₃×C₃₁	C₃×C₁₉
LCS	G ▷ C₂²×C₃₁
UCS	C₁ ◁ C₃×C₁₉

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10602

Conjugacy classes & character table

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 52);