Finite Group Databasebeta

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D₇×C₁₉×C₁₂₁ #44565678

order	32186
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₁₂₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₁₉×C₁₂₁
unambiguous semidirect product	C₇⋊(C₂×C₁₉×C₁₂₁)

Splittings

Fitting, Hall	C₇×C₁₉×C₁₂₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₁₉×C₁₂₁
Hall	C₇×C₁₂₁ ⋊ C₂×C₁₉
Hall	C₇×C₁₉ ⋊ C₂×C₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₁₂₁	D₇
commutator, hypocenter	C₇	C₂×C₁₉×C₁₂₁
Frattini	C₁₁	C₁₁×D₇×C₁₉
Fitting	C₇×C₁₉×C₁₂₁	C₂
socle	C₇×C₁₁×C₁₉	C₂×C₁₁
prime radical	C₁₁×D₇×C₁₉	C₁₁
cosocle	C₇×C₁₁	C₂×C₁₁×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₉×C₁₂₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16093

Conjugacy classes & character table

11495 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32186, 5);