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C₅×C₁₁×C₁₆×C₂₇ #72201072

order	23760
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄²×C₅×C₉ (order 5760) · Inn(G) = C₁ · Out(G) = C₂³×C₄²×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₃₇₆₀
abelian	C₅×C₁₁×C₁₆×C₂₇
multiplicative	(ℤ/23761)ˣ, (ℤ/47522)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₉	C₂×C₃×C₅×C₁₁
socle, prime radical	C₂×C₃×C₅×C₁₁	C₈×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

23760 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₁₈₈₀, D₂₃₇₆₀
maximal subgroup of	Dic₁₁₈₈₀, D₂₃₇₆₀
maximal normal subgroup of	Dic₁₁₈₈₀, D₂₃₇₆₀
automorphism group of	C₂₃₇₆₁
outer automorphism group of	C₂₃₇₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.