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C₂²×C₄×C₈²×C₁₁ #72189779

order	11264
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 193273528320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁷×C₄²×C₈

Aliases

abelian	C₂²×C₄×C₈²×C₁₁
multiplicative	(ℤ/42720)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄²	C₂⁵×C₁₁
socle, prime radical	C₂⁵×C₁₁	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

25194 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₈×C₁₁×C₁₆, C₂²×C₈³×C₁₁, C₂×C₄²×C₈²×C₁₁, …
maximal normal subgroup of	C₂²×C₄×C₈×C₁₁×C₁₆, C₂²×C₈³×C₁₁, C₂×C₄²×C₈²×C₁₁, …
maximal quotient of	C₂²×C₄×C₈×C₁₁×C₁₆, C₂²×C₈³×C₁₁, C₂×C₄²×C₈²×C₁₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.