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C₂²×C₃²×C₄×C₇₃ #72189124

order	10512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 663552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

abelian	C₂²×C₃²×C₄×C₇₃
multiplicative	(ℤ/15365)ˣ, (ℤ/17121)ˣ, (ℤ/18417)ˣ, (ℤ/18459)ˣ, (ℤ/19755)ˣ, (ℤ/22828)ˣ, (ℤ/24556)ˣ, (ℤ/30730)ˣ, (ℤ/31572)ˣ, (ℤ/34242)ˣ, (ℤ/36834)ˣ, (ℤ/36918)ˣ, (ℤ/39510)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃²×C₇₃
socle, prime radical	C₂³×C₃²×C₇₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₈×C₇₃, C₂×C₃²×C₄²×C₇₃, C₂³×C₃²×C₄×C₇₃, …
maximal normal subgroup of	C₂²×C₃²×C₈×C₇₃, C₂×C₃²×C₄²×C₇₃, C₂³×C₃²×C₄×C₇₃, …
maximal quotient of	C₂²×C₃²×C₈×C₇₃, C₂×C₃²×C₄²×C₇₃, C₂³×C₃²×C₄×C₇₃, …
automorphism group of	C₅×C₇×C₄₃₉
outer automorphism group of	C₅×C₇×C₄₃₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.