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C₂²×C₁₆×C₆₄ #72183642

order	4096
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 100663296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₁₆

Aliases

abelian	C₂²×C₁₆×C₆₄
multiplicative	(ℤ/13056)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₃₂	C₂⁴
socle, prime radical	C₂⁴	C₈×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₈×C₃₂ ▷ C₄×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

2795 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₁₆×C₁₂₈, C₂²×C₃₂×C₆₄, C₂×C₄×C₁₆×C₆₄, …
maximal normal subgroup of	C₂²×C₁₆×C₁₂₈, C₂²×C₃₂×C₆₄, C₂×C₄×C₁₆×C₆₄, …
maximal quotient of	C₂²×C₁₆×C₁₂₈, C₂²×C₃₂×C₆₄, C₂×C₄×C₁₆×C₆₄, …
automorphism group of	C₃×C₁₇×C₂₅₆
outer automorphism group of	C₃×C₁₇×C₂₅₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.