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C₂×C₃²×C₈×C₈₃ #72190358

order	11952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 62976
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃²×C₈×C₈₃
multiplicative	(ℤ/13951)ˣ, (ℤ/17937)ˣ, (ℤ/27902)ˣ, (ℤ/35874)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃²×C₈₃
socle, prime radical	C₂²×C₃²×C₈₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

132 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	C₂×C₃²×C₁₆×C₈₃, C₃²×C₄×C₈×C₈₃, C₂²×C₃²×C₈×C₈₃
maximal normal subgroup of	C₂×C₃²×C₁₆×C₈₃, C₃²×C₄×C₈×C₈₃, C₂²×C₃²×C₈×C₈₃
maximal quotient of	C₂×C₃²×C₁₆×C₈₃, C₃²×C₄×C₈×C₈₃, C₂²×C₃²×C₈×C₈₃
automorphism group of	C₇×C₁₉₉₃
outer automorphism group of	C₇×C₁₉₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.