Finite Group Databasebeta

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C₂²×C₃³×C₈×C₁₆ #72192026

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 35332816896
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₃³×C₈

Aliases

C₂²×C₃³×C₈×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂⁴×C₃³
socle, prime radical	C₂⁴×C₃³	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

26936 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃³×C₈×C₃₂, C₂²×C₃³×C₁₆², C₂×C₃³×C₄×C₈×C₁₆, …
maximal normal subgroup of	C₂²×C₃³×C₈×C₃₂, C₂²×C₃³×C₁₆², C₂×C₃³×C₄×C₈×C₁₆, …
maximal quotient of	C₂²×C₃³×C₈×C₃₂, C₂²×C₃³×C₁₆², C₂×C₃³×C₄×C₈×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.