Finite Group Databasebeta

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C₂×C₄²×C₁₆×C₃₂ #72194366

order	16384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 52776558133248
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁴×C₄⁵×C₁₆

Aliases

C₂×C₄²×C₁₆×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈×C₁₆	C₂⁵
socle, prime radical	C₂⁵	C₂²×C₈×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂²×C₈×C₁₆ ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

171393 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₁₆×C₆₄, C₂×C₄²×C₃₂², C₂×C₄×C₈×C₁₆×C₃₂, …
maximal normal subgroup of	C₂×C₄²×C₁₆×C₆₄, C₂×C₄²×C₃₂², C₂×C₄×C₈×C₁₆×C₃₂, …
maximal quotient of	C₂×C₄²×C₁₆×C₆₄, C₂×C₄²×C₃₂², C₂×C₄×C₈×C₁₆×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.