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C₂²×C₃²×C₄×C₈₃ #72190362

order	11952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 755712
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

abelian	C₂²×C₃²×C₄×C₈₃
multiplicative	(ℤ/15197)ˣ, (ℤ/17465)ˣ, (ℤ/19461)ˣ, (ℤ/19539)ˣ, (ℤ/20937)ˣ, (ℤ/22455)ˣ, (ℤ/25948)ˣ, (ℤ/27916)ˣ, (ℤ/30394)ˣ, (ℤ/34930)ˣ, (ℤ/35892)ˣ, (ℤ/38922)ˣ, (ℤ/39078)ˣ, (ℤ/41874)ˣ, (ℤ/44910)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃²×C₈₃
socle, prime radical	C₂³×C₃²×C₈₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11952 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₈×C₈₃, C₂×C₃²×C₄²×C₈₃, C₂³×C₃²×C₄×C₈₃
maximal normal subgroup of	C₂²×C₃²×C₈×C₈₃, C₂×C₃²×C₄²×C₈₃, C₂³×C₃²×C₄×C₈₃
maximal quotient of	C₂²×C₃²×C₈×C₈₃, C₂×C₃²×C₄²×C₈₃, C₂³×C₃²×C₄×C₈₃
automorphism group of	C₇×C₁₃×C₁₆₇, C₅×C₇×C₄₉₉
outer automorphism group of	C₇×C₁₃×C₁₆₇, C₅×C₇×C₄₉₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.