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C₂³×C₃×C₉×C₂₇ #72185087

order	5832
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 238085568
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃²×C₉

Aliases

abelian	C₂³×C₃×C₉×C₂₇
multiplicative	(ℤ/10773)ˣ, (ℤ/21546)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₉	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

3232 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄×C₉×C₂₇, C₂⁴×C₃×C₉×C₂₇, C₂³×C₃×C₉×C₈₁, …
maximal normal subgroup of	C₂²×C₃×C₄×C₉×C₂₇, C₂⁴×C₃×C₉×C₂₇, C₂³×C₃×C₉×C₈₁, …
maximal quotient of	C₂²×C₃×C₄×C₉×C₂₇, C₂⁴×C₃×C₉×C₂₇, C₂³×C₃×C₉×C₈₁, …
automorphism group of	C₇×C₁₉×C₈₁, C₂×C₇×C₁₉×C₈₁
outer automorphism group of	C₇×C₁₉×C₈₁, C₂×C₇×C₁₉×C₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.