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C₂²×C₂₇×C₈₁ #72187604

order	8748
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4251528
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₂₇

Aliases

abelian	C₂²×C₂₇×C₈₁
multiplicative	(ℤ/13203)ˣ, (ℤ/26406)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉×C₂₇	C₂²×C₃²
socle, prime radical	C₂²×C₃²	C₉×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

580 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8748 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₂₇×C₈₁, C₂³×C₂₇×C₈₁, C₂²×C₂₇×C₂₄₃, …
maximal normal subgroup of	C₂×C₄×C₂₇×C₈₁, C₂³×C₂₇×C₈₁, C₂²×C₂₇×C₂₄₃, …
maximal quotient of	C₂×C₄×C₂₇×C₈₁, C₂³×C₂₇×C₈₁, C₂²×C₂₇×C₂₄₃, …
automorphism group of	C₈₁×C₁₆₃, C₂×C₈₁×C₁₆₃
outer automorphism group of	C₈₁×C₁₆₃, C₂×C₈₁×C₁₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.