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C₂³×C₃²×C₄²×C₈ #72188015

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 207807697649664
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₃×C₄³

Aliases

abelian	C₂³×C₃²×C₄²×C₈
multiplicative	(ℤ/43680)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

334206 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×C₄²×C₁₆, C₂³×C₃²×C₄×C₈², C₂²×C₃²×C₄³×C₈, …
maximal normal subgroup of	C₂³×C₃²×C₄²×C₁₆, C₂³×C₃²×C₄×C₈², C₂²×C₃²×C₄³×C₈, …
maximal quotient of	C₂³×C₃²×C₄²×C₁₆, C₂³×C₃²×C₄×C₈², C₂²×C₃²×C₄³×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.