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C₂×C₉×C₁₉×D₃₁ #35234367

order	21204
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₁₉×D₃₁

Splittings

Fitting	C₂×C₉×C₁₉×C₃₁ ⋊ C₂
derived, Sylow	C₃₁ ⋊ C₂²×C₉×C₁₉
Hall	C₉×C₁₉×C₃₁ ⋊ C₂²
Hall	C₁₉×C₃₁ ⋊ C₂²×C₉
Hall	C₉×C₃₁ ⋊ C₂²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₃₁
commutator, hypocenter	C₃₁	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×D₃₁
Fitting	C₂×C₉×C₁₉×C₃₁	C₂
socle	C₂×C₃×C₁₉×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₁₉×D₃₁	C₃
cosocle	C₃×C₃₁	C₂²×C₃×C₁₉
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₉×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10602

Conjugacy classes & character table

5814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 64);