Finite Group Databasebeta

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C₂³×C₃×C₄³×C₉ #72192061

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 409121404747776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₃×C₄³

Aliases

abelian	C₂³×C₃×C₄³×C₉
multiplicative	(ℤ/57720)ˣ, (ℤ/59280)ˣ, (ℤ/62160)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₃	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₂³×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

338580 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	C₂³×C₃×C₄²×C₈×C₉, C₂²×C₃×C₄⁴×C₉, C₂⁴×C₃×C₄³×C₉
maximal normal subgroup of	C₂³×C₃×C₄²×C₈×C₉, C₂²×C₃×C₄⁴×C₉, C₂⁴×C₃×C₄³×C₉
maximal quotient of	C₂³×C₃×C₄²×C₈×C₉, C₂²×C₃×C₄⁴×C₉, C₂⁴×C₃×C₄³×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.