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C₂³×C₃²×C₈×C₁₆ #72187995

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 67645734912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₃×C₈

Aliases

abelian	C₂³×C₃²×C₈×C₁₆
multiplicative	(ℤ/34272)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

36030 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃²×C₈×C₃₂, C₂³×C₃²×C₁₆², C₂²×C₃²×C₄×C₈×C₁₆, …
maximal normal subgroup of	C₂³×C₃²×C₈×C₃₂, C₂³×C₃²×C₁₆², C₂²×C₃²×C₄×C₈×C₁₆, …
maximal quotient of	C₂³×C₃²×C₈×C₃₂, C₂³×C₃²×C₁₆², C₂²×C₃²×C₄×C₈×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.