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C₂³×C₉×C₈₃ #72185175

order	5976
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 82656
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂³×C₉×C₈₃
multiplicative	(ℤ/9519)ˣ, (ℤ/12692)ˣ, (ℤ/18036)ˣ, (ℤ/19038)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₈₃
socle, prime radical	C₂³×C₃×C₈₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5976 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₉×C₈₃, C₂⁴×C₉×C₈₃, C₂³×C₂₇×C₈₃, …
maximal normal subgroup of	C₂²×C₄×C₉×C₈₃, C₂⁴×C₉×C₈₃, C₂³×C₂₇×C₈₃, …
maximal quotient of	C₂²×C₄×C₉×C₈₃, C₂⁴×C₉×C₈₃, C₂³×C₂₇×C₈₃, …
automorphism group of	C₃×C₁₉×C₁₆₇, C₄×C₂₇×C₁₆₇
outer automorphism group of	C₃×C₁₉×C₁₆₇, C₄×C₂₇×C₁₆₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.