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C₂×C₄²×C₃₆₁ #72190000

order	11552
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 525312
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄²×C₃₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₉	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₂²×C₁₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11552 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₈×C₃₆₁, C₄³×C₃₆₁, C₂²×C₄²×C₃₆₁
maximal normal subgroup of	C₂×C₄×C₈×C₃₆₁, C₄³×C₃₆₁, C₂²×C₄²×C₃₆₁
maximal quotient of	C₂×C₄×C₈×C₃₆₁, C₄³×C₃₆₁, C₂²×C₄²×C₃₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.