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C₂²×C₄×C₅²×C₃₂ #72191122

order	12800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 377487360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄×C₅

Aliases

abelian	C₂²×C₄×C₅²×C₃₂
multiplicative	(ℤ/35200)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂⁴×C₅²
socle, prime radical	C₂⁴×C₅²	C₂×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

5136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₅²×C₆₄, C₂²×C₅²×C₈×C₃₂, C₂×C₄²×C₅²×C₃₂, …
maximal normal subgroup of	C₂²×C₄×C₅²×C₆₄, C₂²×C₅²×C₈×C₃₂, C₂×C₄²×C₅²×C₃₂, …
maximal quotient of	C₂²×C₄×C₅²×C₆₄, C₂²×C₅²×C₈×C₃₂, C₂×C₄²×C₅²×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.