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C₅×C₈×C₃₇₃ #72193000

order	14920
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₃₁ (order 5952) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₃₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₉₂₀
abelian	C₅×C₈×C₃₇₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₃₇₃
socle, prime radical	C₂×C₅×C₃₇₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14920 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₉₂₀, D₂₉₈₄₀
Fitting subgroup of	D₁₄₉₂₀, Dic₇₄₆₀
maximal subgroup of	C₅×C₁₆×C₃₇₃, C₂×C₅×C₈×C₃₇₃, D₁₄₉₂₀, …
maximal normal subgroup of	C₅×C₁₆×C₃₇₃, C₂×C₅×C₈×C₃₇₃, D₁₄₉₂₀, …
maximal quotient of	C₅×C₁₆×C₃₇₃, C₂×C₅×C₈×C₃₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.