Finite Group Databasebeta

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C₂×C₃×C₄×C₉×C₇₃ #72193763

order	15768
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 62208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃×C₄×C₉×C₇₃
multiplicative	(ℤ/16243)ˣ, (ℤ/16663)ˣ, (ℤ/23679)ˣ, (ℤ/32486)ˣ, (ℤ/33326)ˣ, (ℤ/47358)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃²×C₇₃
socle, prime radical	C₂²×C₃²×C₇₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15768 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₉×C₇₃, C₃×C₄²×C₉×C₇₃, C₂²×C₃×C₄×C₉×C₇₃
maximal normal subgroup of	C₂×C₃×C₈×C₉×C₇₃, C₃×C₄²×C₉×C₇₃, C₂²×C₃×C₄×C₉×C₇₃
maximal quotient of	C₂×C₃×C₈×C₉×C₇₃, C₃×C₄²×C₉×C₇₃, C₂²×C₃×C₄×C₉×C₇₃
automorphism group of	C₃₇×C₄₃₉, C₁₉×C₈₇₇
outer automorphism group of	C₃₇×C₄₃₉, C₁₉×C₈₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.