Finite Group Databasebeta

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C₅×C₈×C₂₇×C₂₉ #72208107

order	31320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄²×C₇×C₉ (order 8064) · Inn(G) = C₁ · Out(G) = C₂³×C₄²×C₇×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₃₂₀
abelian	C₅×C₈×C₂₇×C₂₉
multiplicative	(ℤ/31321)ˣ, (ℤ/62642)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₅×C₂₉
socle, prime radical	C₂×C₃×C₅×C₂₉	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

31320 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₆₆₀, D₃₁₃₂₀
maximal subgroup of	Dic₁₅₆₆₀, D₃₁₃₂₀
maximal normal subgroup of	Dic₁₅₆₆₀, D₃₁₃₂₀
automorphism group of	C₃₁₃₂₁
outer automorphism group of	C₃₁₃₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.